Sum of squares

The product of two numbers is 12. If the sum of their squares is 40, find the numbers.

Correct answer:

a =  6
b =  2

Step-by-step explanation:

ab=12 a2+b2 = 40  a2+(12/a)2 = 40  a4+122 = 40 a2  z = a2  z2+122=40 z  z2+122=40 z z240z+144=0  a=1;b=40;c=144 D=b24ac=40241144=1024 D>0  z1,2=2ab±D=240±1024 z1,2=240±32 z1,2=20±16 z1=36 z2=4  z>0  a=z1=36=6

Our quadratic equation calculator calculates it.

b=12/a=12/6=2   Verifying Solution:  p=a b=6 2=12 s=a2+b2=62+22=40



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