Question

2f x+1/x=6 find x^4+1/x^4

class 9​

Answer 1

EXPLANATION.

⇒ (x + 1/x) = 6.

As we know that,

Squaring on both sides of the equation, we get.

⇒ (x + 1/x)² = (6)².

⇒ x² + (1/x)² + 2(x)(1/x) = 36.

⇒ x² + 1/x² + 2 = 36.

⇒ x² + 1/x² = 36 - 2.

⇒ x² + 1/x² = 34.

Again squaring on both sides of the equation, we get.

⇒ (x² + 1/x²)² = (34)².

⇒ (x²)² + (1/x²)² + 2(x²)(1/x²) = 1156.

⇒ x⁴ + 1/x⁴ + 2 = 1156.

⇒ x⁴ + 1/x⁴ = 1156 - 2.

⇒ x⁴ + 1/x⁴ = 1154.

Answer 2

Step-by-step explanation:

$if \: x + \frac{1}{x} = 6 \: find \: {x}^{4} + \frac{1}{ {x}^{4} }$

Short trick :-

Formula :-

$if \: \: x + \frac{1}{x} = y$

$then \: \: {x}^{4} + \frac{1}{ {x}^{4} } = {y}^{2} - 4y² + 2$

$so \: \: \: {x}^{4} + \frac{1}{ {x}^{4} } = {6}^{4} - 4(6)² +2$

= 1296 – 4 × 36 + 2

= 1296 – 144 +2

$= 1246 – 142$

$=1154$

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