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If $3 left parenthesis straight a squared plus straight b squared plus straight c squared right parenthesis space equals space left parenthesis straight a plus straight b plus straight c right parenthesis squared comma space$ then the relation between a, b and c is

$straight a not equal to straight b not equal to straight c$
$straight a equals space straight b space not equal to space straight c$
$straight a not equal to straight b equals straight c$
$straight a not equal to straight b equals straight c$

141 Views

112.

If $straight x minus square root of 3 minus square root of 2 space equals space 0$ and $straight y minus square root of 3 plus square root of 2 space space equals space 0 comma$ then the value of $left parenthesis straight x cubed minus 20 square root of 2 right parenthesis space minus space left parenthesis straight y cubed space plus space 2 square root of 2 right parenthesis$ is

139 Views

113.

If $straight a minus fraction numerator 1 over denominator straight a minus 3 end fraction space equals space 5$ , then the value of $left parenthesis straight a minus 3 right parenthesis cubed space minus space fraction numerator 1 over denominator left parenthesis straight a minus 3 right parenthesis cubed end fraction$ is

153 Views

114.
Let $straight x space equals space fraction numerator square root of 13 space plus space square root of 11 over denominator square root of 13 space minus square root of 11 end fraction$ and $straight y space equals space 1 over straight x comma$ then the value of $3 straight x squared space minus space 5 xy space plus space 3 straight y squared$ is

1717

1177

1771

1771

1717

straight x space equals space fraction numerator square root of 13 minus square root of 11 over denominator square root of 13 space plus space square root of 11 end fraction space space space comma space space straight y space equals space 1 over straight x space equals space fraction numerator square root of 13 plus square root of 11 over denominator square root of 13 minus square root of 11 end fraction

straight x space plus space straight y space equals space fraction numerator square root of 13 minus square root of 11 over denominator square root of 13 plus square root of 11 end fraction space plus space fraction numerator square root of 13 plus square root of 11 over denominator square root of 13 minus square root of 11 end fraction space space space space space space space space space space equals space fraction numerator left parenthesis 13 plus 11 right parenthesis over denominator left parenthesis 13 minus 11 right parenthesis end fraction cross times 2 space equals space 24 over 2 space cross times space 2 space equals space 24

straight x. space straight y space equals space fraction numerator square root of 13 minus square root of 11 over denominator square root of 13 space plus space square root of 11 end fraction space space cross times space fraction numerator square root of 13 space plus square root of 11 over denominator square root of 13 minus square root of 11 end fraction space equals space 1

3 straight x squared minus 5 xy plus 3 straight y squared space equals space 3 left parenthesis straight x plus straight y right parenthesis squared minus 11 xy space equals space 3 left parenthesis 24 right parenthesis squared space minus 11 space left parenthesis 1 right parenthesis space equals space 1717

191 Views

115.

If x² + y² + z² = xy + yz + zx, then the value of
$fraction numerator 3 straight x to the power of 4 space plus space 7 straight y to the power of 4 space plus space 5 straight z to the power of 4 over denominator 5 straight x squared straight y squared space plus space 7 straight y squared straight z squared space plus space 3 straight z squared straight x squared end fraction$ is

152 Views

116.

If $straight x space equals space straight a to the power of 1 half end exponent space plus space straight a to the power of negative 1 half end exponent comma space space space straight y space equals space straight a to the power of 1 half end exponent space minus space straight a to the power of negative 1 half end exponent$ then value of $left parenthesis straight x to the power of 4 minus straight x squared straight y squared minus 1 right parenthesis plus space left parenthesis straight y to the power of 4 minus straight x squared straight y squared plus 1 right parenthesis$ is

160 Views

117.

If $straight a plus 1 over straight b space equals space straight b space plus space 1 over straight c space equals space straight c space plus 1 over straight a comma$ where $straight a not equal to straight b not equal to straight c not equal to 0 comma$ then the value of a²b²c² is

-1
abc
0
0

167 Views

118.

If a + b = 1, find the value of a³ + b³ - ab - (a² - b²)².

-1
1
0
0

164 Views

119.

If $open parentheses fraction numerator straight p to the power of negative 1 end exponent straight q squared over denominator straight p cubed straight q to the power of negative 2 end exponent end fraction close parentheses to the power of 1 third end exponent space divided by space open parentheses fraction numerator straight p to the power of 6 straight q to the power of negative 3 end exponent over denominator straight p to the power of negative 2 end exponent straight q cubed end fraction close parentheses to the power of 1 third end exponent space equals space straight p to the power of straight a space straight q to the power of straight b$ , then the value of a + b, where p and q are different positive primes is

$fraction numerator negative 2 over denominator 3 end fraction$
2
1
1

145 Views

120.

If $open parentheses straight a plus 1 over straight a close parentheses space equals space minus 2 comma$ then the value of $straight a to the power of 1000 plus space straight a to the power of negative 1000 end exponent$ is