if x - 1/x = 7, then find the value of x² + 1/x²
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Answer:
x²+1/x² = 51
Explanation:
Given x - 1/x = 7 ---(1)
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We know the algebraic identity:
a²+b²-2ab = (a-b)²
Or
a²+b² = (a-b)²+2ab
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Now,
x²+1/x²
= (x-1/x)²+2*x*(1/x)
= (x-1/x)²+2
= 7²+2 [ from (1)]
= 49+2
= 51
Therefore,
x²+1/x² = 51
Step-by-step explanation:
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