Question

if x+1/x=11 find the value of x⁴+1/x⁴


Plz answer fast​

Answer 1

Given:

x + (1/x) = 11

(a + b)^4 = a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4

Rearranging the above equation, we get

a^4 + b^4 = (a + b)^4 - 4*a^3*b - 4*a*b^3 - 6*a^2*b^2

a^4 + b^4 = (a + b)^4 - 4*a*b(a^2 + b^2) - 6*a^2*b^2

a^4 + b^4 = (a + b)^4 - 4*a*b((a + b)^2 -2*a*b) - 6*a^2*b^2

Since (a^2 + b^2) = ((a + b)^2 -2*a*b)

a^4 + b^4 = (a + b)^4 - 4*a*b(a + b)^2 + 8*a^2*b^2 - 6*a^2*b^2

a^4 + b^4 = (a + b)^4 - 4*a*b(a + b)^2 + 8*a^2*b^2 - 6*a^2*b^2

a^4 + b^4 = (a + b)^4 - 4*a*b(a + b)^2 + 2*a^2*b^2

Let a = x & b = 1/x

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

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

Substituting x + (1/x) = 11 in the above equation, we get

x^4 + (1/x)^4 = 11^4 - 4*11^2 + 2

x^4 + (1/x)^4 = 14641 - 428 + 2

x^4 + (1/x)^4 = 14215 ——> Answer