Question

Determine the value of a^2 +b^2+c^2, if a+b+c=7 and ab+bc+ca=15​

Answer 1

`\huge\boxed{\sf a^2+b^2+c^2 = 19}`

Explanation:

`\sf (a+b+c)^2 = a^2+b^2+c^2 +2(ab+bc+ca)\\\\Put \ a+b+c = 7 \ and \ ab+bc+ca = 15\\\\7^2 = a^2+b^2+c^2 + 2(15)\\\\ 49 = a^2+b^2+c^2 + 30\\\\49 - 30 = a^2+b^2 +c^2\\\\a^2+b^2+c^2 = 19\\\\\rule[225]{225}{2}`

Hope this helped!

~AH1807