If x^24 + 1 / x^12 = 7 then the value of x^72 + 1 / x^36 is
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(x24 + 1)/x12 = 7
x24/x12 + 1/ x12 = 7
x12 + 1/x12 = 7. ……………. (1)
Cube on both sides,
(x12 + 1/ x12)3 = 7^3
(x12)3 + (1/x12)3 + 3 (x12 + 1/x12) = 7^3
x36 + 1/x36 + 3 x 7 = 343 (from equation 1)
x36 + 1/x36 = 343 – 21
x36 + 1/x36 = 322
x24/x12 + 1/ x12 = 7
x12 + 1/x12 = 7. ……………. (1)
Cube on both sides,
(x12 + 1/ x12)3 = 7^3
(x12)3 + (1/x12)3 + 3 (x12 + 1/x12) = 7^3
x36 + 1/x36 + 3 x 7 = 343 (from equation 1)
x36 + 1/x36 = 343 – 21
x36 + 1/x36 = 322
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