Question

8. If x2 + 1/x2 =7 and x ¥ 0 . Find the value of;

7x3 +8x - 7/x3 - 8/x .


ans is + 64
$+ 64 \sqrt{5}$
​

Answer 1

Solution:

Given x²+1/x² = 7

=> x²+1/x²-2 = 7-2

=> (x-1/x)² = 5

=> x - 1/x = √5 ---(1)

i) x³-1/x³ = (x-1/x)³+3(x-1/x)

= (√5)³+3(√5) /* from (1) */

= 5√5 +3√5

= 8√5 ----(2)

ii ) Now ,

7x³+8x-7/x³-8/x

= 7x³-7/x³ + 8x-8/x

= 7(x³-1/x³)+8(x-1/x)

=7(8√5) + 8(√5)

= 56√5 +8√5

= (56+8)√5

= 64√5

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