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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

0

1

3

3

straight x minus square root of 3 space minus space square root of 2 space equals space 0 rightwards double arrow space space straight x space equals space square root of 3 space plus space square root of 2

Again,

straight y space minus square root of 3 space plus space square root of 2 space equals space 0 rightwards double arrow space space space straight y space equals space square root of 3 space minus space square root of 2 therefore space space straight x space minus space straight y space equals space square root of 3 space plus space square root of 2 space minus space square root of 3 space plus space square root of 2 space equals space 2 square root of 2

and

xy space equals space open parentheses square root of 3 space plus space square root of 2 close parentheses space left parenthesis square root of 3 space minus space square root of 2 right parenthesis space equals space 3 minus space 2 space equals space 1

∴ Expression

equals space straight x cubed minus 20 square root of 2 space minus space straight y cubed minus 2 square root of 2 equals space straight x cubed minus straight y cubed minus 22 square root of 2 equals space left parenthesis straight x minus straight y right parenthesis cubed plus 3 xy left parenthesis straight x minus straight y right parenthesis minus 22 square root of 2 equals space left parenthesis 2 square root of 2 right parenthesis cubed space plus space 3 left parenthesis 2 square root of 2 right parenthesis space minus space 22 square root of 2 equals space 16 square root of 2 space plus space 6 square root of 2 space minus 22 square root of 2 space equals space 0

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

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

262 Views

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112. If and then the value of is 0 1 3 3