Question

X^4+x^-4=194 find value of
then(x-2)^2

Answer 1

If $x^{4} + x^{- 4} = 194\\, then the value of (x -2)^{2} =3.</strong></h2><p><strong>Step-by-step explanation:</strong></p><p>Given, [tex]x^{4} + x^{- 4} = 194</p><p>⇒ [tex]x^{2} + x^{- 2} = 194 + 2 = [tex]\sqrt{196\\}$ =14

⇒ x + $\frac{1}{x}$ =$\sqrt{16\\}$ = 4

⇒ $(x - 2) ^{2}$ = $x^{2}$ - 4\times{x} + 4

= 0 + 3 =3

Hence, the value of $(x - 2) ^{2}$  = 3.