If(x2+1/x2)=79 then find the value of x+1/x
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Answered by
10
Answer:
We know that, (x + 1/x)^2 = x^2 + 1/x^2 + 2x + 1/x
Given , x^2 + 1/x^2 = 79
So, (x + 1/x)^2 = 79 + 2
(x + 1/x)^2 = 81
(x + 1/x ) = 9
Step-by-step explanation:
Hope it helped u dear frnd!!
Answered by
4
Given, x+1/x = 9 , Squaring both sides
(x+1/x)² = 81 ……………………………………………………..(1)
Now we have
(x- 1/x)² = x² - 2.x.1/x + (1/x)² = x² - 2+ 1/x²
Or, (x- 1/x)² = x² + 2 -2 - 2+ 1/x² (Adding and subtracting 2)
Or, (x- 1/x)² = x² + 2.1 - 4+ 1/x² = x² + 2.x.1/x - 4+ 1/x²
= (x² + 2.x.1/x + 1/x²) - 4 = (x+1/x)² - 4
Substituting for (x+1/x)² from (1),
(x- 1/x)² = 81 - 4 = 77 , Taking square root of both sides
⇒ x- 1/x = ±77½ or ±8.775 (rounded to third decimal) (Answer)
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