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If $straight a plus 1 over straight a plus 2 space equals space 0 comma$ then the value of $open parentheses straight a to the power of 37 minus 1 over straight a to the power of 100 close parentheses$ is

0
-2
1
1

129 Views

92.

If a + b + c = 0, then the value of $fraction numerator straight a squared plus space straight b squared space plus space straight c squared over denominator straight a squared space minus bc end fraction$ is

103 Views

93.
If a + b + c = 6, a² + b² + c² = 14 and a³ + b³ + c³ = 36, then the value of abc is

3

6

9

9

(a + b + c)²
$left parenthesis straight a plus straight b plus straight c right parenthesis squared equals space space straight a squared space plus space straight b squared space plus space straight c squared space space plus space 2 left parenthesis ab space plus space bc space plus space ca right parenthesis rightwards double arrow space space 36 space equals space space 14 space plus space 2 left parenthesis ab space plus space bc space plus space ca right parenthesis rightwards double arrow space space space space ab space plus space bc space plus space ca space equals space left parenthesis 36 minus 14 right parenthesis space divided by space 2 rightwards double arrow space space space space ab space space plus space bc space plus space ca space equals space 11$

$therefore space space straight a cubed space plus space straight b cubed space plus space straight c cubed space minus space 3 abc space equals space left parenthesis straight a plus straight b plus straight c right parenthesis thin space left parenthesis straight a squared plus straight b squared plus straight c squared minus ab minus bc minus ca right parenthesis rightwards double arrow space space space space space space space space 36 space minus space 3 abc space equals space 6 left parenthesis 14 minus 11 right parenthesis rightwards double arrow space space space space space space space 36 space minus space 3 abc space equals space 84 space minus space 66 space equals space 18 rightwards double arrow space space space space space space 3 abc space equals space 36 minus 18 space equals space 18 rightwards double arrow space space space space space space abc space equals space space 6$

175 Views

94.

If $open parentheses straight x plus 1 over straight x close parentheses squared space equals space 3$ , then the value of (x⁷² + x⁶⁶ + x⁵⁴ + x³⁶ + x²⁴ + x⁶ +1) is

128 Views

95.

If $open parentheses straight x plus 1 over straight x close parentheses squared space equals space 3 comma$ then the value of x²⁰⁶ + x²⁰⁰ + x⁹⁰ + x⁸⁴ + x¹⁸ + x¹² + x⁶ + 1 is

117 Views

96.

If $straight n space equals space 7 space plus space 4 square root of 3 comma$ then the value of $open parentheses square root of straight n plus fraction numerator 1 over denominator square root of straight n end fraction close parentheses$ is

$2 square root of 3$
4
-4
-4

90 Views

97.

P varies inversely with the product of Q and R. When Q = 6 and R = 12, P = 75. When Q = 5, R = 10, then P is

256 Views

98.

If a³b = abc = 180, a, b, c are positive integers, then the value of c is

1054 Views

99.

If $open parentheses straight x plus 1 over straight x close parentheses squared space equals space 3$ , then $open parentheses straight x cubed space plus space 1 over straight x cubed close parentheses$ is equal to

153 Views

100.

If $straight x plus 1 over straight x space equals space 2$ , then the value of $straight x to the power of 100 space plus space 1 over straight x to the power of 100$ is