Math, asked by Anonymous, 2 months ago

if x+1/x = 3 find x⁴+1/x⁴

Answers

Answered by sumairadoll
1

Step-by-step explanation:

x+1/x=3

taking square on both sides

(x+1/x)²=3²

x²+1/x²+2(x)(1/x)=9

x²+1/x²+2=9

x²+1/x²=9-2

x²+1/x²=7

again taking square on both sides

(x²+1/x²)²=7²

x⁴+1/x⁴+2(x²)(1/x²)=49

x⁴+1/x⁴+2=49

x⁴+1/x⁴=49-2

x⁴+1/x⁴=47

Answered by phaneendranv001
0

Answer:

x^4 + 1/x^4= 47

Step-by-step explanation:

Given:

x+1/x = 3

Therefore, (x+1/x)^2= x^{2} + 1/x^2 + 2(x)(1/x)

(3)^2 = x^{2} + 1/x^2 + 2

⇒ 9 = x^{2} + 1/x^2 + 2

x^{2} + 1/x^2=7                                                          __ 1

So,

(x^2 + 1/x^2)^2= x^4 + 1/x^4 + 2 (x^2)(1/x^2)

⇒ (7)² =x^4 + 1/x^4+ 2

⇒ 49 =  x^4 + 1/x^4 + 2

x^4 + 1/x^4 = 47

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