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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

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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

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93.

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

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

straight n space equals space 7 plus 4 square root of 3 space equals space 7 space plus space 2 space cross times space 2 space cross times space square root of 3 space equals space 4 space plus space 3 space plus 2 space cross times space 2 space cross times space square root of 3 straight n space equals space left parenthesis 2 plus square root of 3 right parenthesis squared

therefore space space square root of straight n space equals space 2 plus space square root of 3 therefore space space space fraction numerator 1 over denominator square root of straight n end fraction space equals space fraction numerator 1 over denominator 2 plus square root of 3 end fraction equals space fraction numerator 1 over denominator 2 plus square root of 3 end fraction space cross times space fraction numerator 2 minus square root of 3 over denominator 2 minus square root of 3 end fraction space equals space 2 minus square root of 3

therefore space space square root of straight n space plus space fraction numerator 1 over denominator square root of straight n end fraction space equals space 2 plus space square root of 3 space plus space 2 minus square root of 3 space equals space 4

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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

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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