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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

0

1

2

2

rightwards double arrow space space space straight a plus straight b plus straight c space equals space 0 rightwards double arrow space space space space straight b space plus space straight c space equals space minus straight a

S.B.S.

rightwards double arrow space space space left parenthesis straight b space plus space straight c right parenthesis squared space equals space straight a squared rightwards double arrow space space straight b squared space plus space straight c squared space plus space 2 bc space equals space straight a squared

Adding a² on both sides.

rightwards double arrow space space straight a squared space plus space straight b squared space plus space straight c squared space plus space 2 bc space equals space 2 straight a squared rightwards double arrow space straight a squared space space plus space straight b squared space plus space straight c squared space equals space 2 straight a squared space minus space 2 bc space equals space 2 left parenthesis straight a squared space minus space bc right parenthesis therefore space space fraction numerator straight a squared plus straight b squared plus straight c squared over denominator straight a squared minus bc end fraction space equals space fraction numerator 2 left parenthesis straight a squared minus bc right parenthesis over denominator straight a squared minus bc end fraction space equals space 2

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

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