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If x+1÷x=6 find X square+1÷X square


User Pmtamal
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1 Answer

2 votes

Answer:


\huge\boxed{\sf x^2+(1)/(x^2) = 34 }

Explanation:

Given:


\displaystyle x + (1)/(x) = 6

Using formula:

(a + b)² = a² + 2ab + b² ----------(1)

Here, a = x and b = 1/x

Put in Eq. (1)


\displaystyle (x + (1)/(x) )^2 = (x)^2+2(x)((1)/(x) )+((1)/(x) )^2\\\\

Given that,
\displaystyle x + (1)/(x) = 6


\displaystyle So,\\\\(6)^2=x^2+2+(1)/(x^2) \\\\36 = x^2+2+(1)/(x^2)

  • Subtract 2 from both sides


\displaystyle 36 - 2 = x^2+(1)/(x^2) \\\\34 = x^2+(1)/(x^2) \\\\x^2+(1)/(x^2) = 34 \\\\\rule[225]{225}{2}

User Enreas
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