Question

if x²+y² = 29 and xy = 2, find the value of

(i) x + y

(ii) x - y

(iii) x⁴ + y⁴

Answer 1

(i) x+y

Given that,

x² + y² = 29

x² + y² + 2xy – 2xy = 29

(x + y)² – 2 (2) = 29

(x + y)² = 29 + 4

x + y = \(\sqrt{33}\)

(ii) x-y

x² + y² = 29

x² + y² + 2xy – 2xy = 29

(x – y)² + 2 (2) = 29

(x – y)² + 4 = 29

(x – y)² = 25

(x – y) = 5

(iii) x⁴+y⁴

x² + y² = 29

Squaring both sides, we get

(x² + y²)² = (29)²

x⁴ + y⁴ + 2x²y² = 841

x⁴ + y⁴ + 2 (2)2 = 841

x⁴ + y⁴ = 841 – 8

x⁴ + y⁴ = 833