Question

If a+b+c=7 and ab+bc+ca=20 find the value of a power 2 +b power2+c power2

Answer 1

ANSWER:

Given

• a + b + c = 7_____ ( 1 )
• ab + bc + ca = 20_____ ( 2 )
• a² + b² + c² = ?

Taking equation 1 and squaring on both sides

(a + b+ c)² = 7²

Using

(x + y + z)² = x² + y² + z² + 2(xy + yz + xz)

→ a² + b² + c² + 2(ab + bc + ca) = 49

→ a² + b² + c² + 2(20) = 49 [°.°equation(2)]

→ a² + b² + c² + 40 = 49

→ a² + b² + c² = 49 - 40

→ a² + b² + c² = 9

Hence, a² + b² + c² = 9