Question

If x + y = 10 and xy = 4, then what is the value of x4 + y4

Answer 1

Xy = 4
x = y/4 -- eq 1

X + y = 10
y/4 + y = 10
y + 4y / 4 =10
5y = 10 × 4
y = 8

x = y/4 = 8/4 = 2

Answer 2

Answer: 8432

Step-by-step explanation:

Given x+y= 10 and xy=4

To find :$x^4+y^4$

we have

$x+y=10 \\\\ \text { Squaring both sides we get }\\\\ (x+y)^2=10^2\\\\\Rightarrow x^2+y^2+2xy = 100\\\\ \text { Put xy=4 then}\\\\\Rightarrow x^2+y^2+2\times4=100\\\\\Rightarrow x^2+y^2=100- 8\\\\\Rightarrow x^2+y^2= 92\\\\ \text { Squaring both sides again we get }\\\\\Rightarrow (x^2+y^2)^2= 92^2\\\\\Rightarrow x^4+y^4+2x^2y^2=8464\\\\\Rightarrow x^4+y^4 = 8464- 2(xy)^2\\\\\Rightarrow x^4+y^4 = 8464-2\times 16\\\\\Rightarrow x^4+y^4 = 8464- 32= 8432$

Hence the value is 8432