Answer to Question #43620 in Algebra for ruchi

Question

if (a-b)=7 and ab=9. then a^2+b^2=_____

Answer 1

To find the answer using the next formula: (a-b)²=a²-2ab+b².
So we know that (a-b)=7, from this we have (a-b)²=49.
On the other hand 49=a²-2ab+b². Substitute here ab=9. We obtain: 49=a²-2*9+b².

Thus, a²+b²=49+18=67.

Answer. 67.