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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

103 Views

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

1

2

3

3

space open parentheses straight x plus 1 over straight x close parentheses squared space equals space 3

therefore space space space straight x plus 1 over straight x space equals square root of 3

If space space straight x space plus 1 over straight x space equals space straight a comma space space then space space straight x cubed space plus space 1 over straight x cubed space equals space straight a cubed space minus space 3 straight a

therefore space space straight x cubed space plus space 1 over straight x cubed space equals space left parenthesis square root of 3 right parenthesis cubed space minus space 3 cross times square root of 3 space equals space 0

rightwards double arrow space space space straight x cubed space plus space 1 over straight x cubed space equals space 0 space space rightwards double arrow space space straight x to the power of 6 space plus space 1 space equals space 0

therefore space space space space space space straight x to the power of 72 space plus space straight x to the power of 66 space plus space straight x to the power of 54 space plus space straight x to the power of 36 space plus space straight x to the power of 24 space plus space straight x to the power of 6 space plus space 1 space space space equals space left parenthesis straight x to the power of 6 right parenthesis to the power of 12 space plus space left parenthesis straight x to the power of 6 right parenthesis to the power of 11 space plus space left parenthesis straight x to the power of 6 right parenthesis to the power of 9 space plus space left parenthesis straight x to the power of 6 right parenthesis to the power of 6 space plus space left parenthesis straight x to the power of 6 right parenthesis to the power of 4 space plus space straight x to the power of 6 space plus space 1 space equals space space 1 minus 1 minus 1 plus 1 plus 1 plus 0 space equals space 1

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

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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

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