Question

if x^2+y^2 = 29 and xy=2 find x^4+y^4​

Answer 1

Answer:

ur answer is 833

(x sq. +y sq )=(29) sq.

x^4+y^4+2(x^2y^2)=841

x^4+y^4+2(xy)^2=841

x^4+y^4+2(2)^2=841

x^4+y^4+8=841

x^4+y^4=841-8=833

hope this helps u

Answer 2

Your Answer:

Given:-

• $\tt x^{2}+y^{2}= 29$

• $\tt xy = 2$

To find:-

• $\tt x^{4}+y^{4}$

Solution:-

$\tt (x^{2}+y^{2})^{2}=(x^{2})^{2}+(y^{2})^{2}+2x^{2}y^{2}\\\\\Rightarrow(x^{2}+y^{2})^{2}-2(xy)^{2}=x^{4}+y^{4}$

Now replacing values

$\tt (x^{2}+y^{2})^{2}-2(xy)^{2}=x^{4}+y^{4}\\\\\Rightarrow(29)^{2}-2(2)^{2}=x^{4}+y^{4}\\\\\Rightarrow841-8=x^{4}+y^{4}\\\\\Rightarrow833=x^{4}+y^{4}$

So,the answer is 833

Additional:-

Here, Some algebraic identities is used

• $\tt (a+b)^{2}=a^{2}+b^{2}+2ab$