Question

If x2+1/x2=27 find the value of x+1/x

Answer 1

x²+1/x² = 27
(x)²+(1/x)²+2(x)(1/x) = 29

using formula ,
a²+b²+2ab = (a+b)²


(x+1/x)² = 29
x+1/x = √29



hope this helps

Answer 2

Answer:

Value of $x+\frac{1}{x}=±\sqrt{29}$

Explanation:

Given $x^{2}+\frac{1}{x^{2}}=27$

$\implies x^{2}+\frac{1}{x^{2}}+2\times x \times \frac{1}{x}\\=27+2\times x \times \frac{1}{x}$

$\implies x^{2}+\frac{1}{x^{2}}+2\times x \times \frac{1}{x}\\=27+2$

$\implies \left(x+\frac{1}{x}\right)^{2}=29$

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By algebraic identity:

$\boxed {a^{2}+2ab+b^{2}=(a+b)^{2}}$

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$\implies x+\frac{1}{x}=±\sqrt{29}$

Therefore,

Value of $x+\frac{1}{x}=±\sqrt{29}$

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