Question

x+1/x =8 find x²+ 1/x²​

Answer 1

Answer:

Step-by-step explanation:

x+1/x=8

(x+1/x)²=x²+1/x²+2x*1/x

8²=x²+1/x²+2

64=x²+1/x²+2

x²+1/x²=62

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Answer 2

$\underline{\textsf{Question :}}$

$\textsf{If}\:\bold{x+\frac{1}{x} =8}$

$\textsf{then}\:x^{2} +\frac{1}{x^{2}} =?$

$\underline{\textsf{Solution :}}$

$\textsf{Given,}\:\:\bold{x+\frac{1}{x} =8}$

$\underline{\textsf{Squaring both side we get}}$

$\implies \bold{x^{2}+\frac{1}{x^{2}} +2*x*\frac{1}{x} =8^{2}}$

$\implies \bold{x^{2} +\frac{1}{x^{2} } +2=64}}$

$\implies \bold{x^{2} +\frac{1}{x^{2} } =64-2}$

$\implies \boxed{\bold{x^{2} +\frac{1}{x^{2}} =62}}$

$\underline{\textsf{Identity Rules :}}$

$1.\:\bold{(a+b)^{2}=a^{2}+2ab+b^{2}}$

$2.\:\bold{(a-b)^{2}=a^{2}-2ab+b^{2}}$

$3.\:\bold{(a+b)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3}}$

$4.\:\bold{(a-b)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3}}$

$5.\:\bold{a^{2}+b^{2}=(a+b)^{2}-2ab}$

$6.\:\bold{a^{2}-b^{2}=(a+b)(a-b)}$