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lesya692 [45]
3 years ago
5

If a square+ b square+ c square=90, a+b+c=20 find the value of ab+bc+ca

Mathematics
1 answer:
DaniilM [7]3 years ago
8 0

Answer: ab + bc + ac = 155

<u>Step-by-step explanation:</u>

Given: a² + b² + c² = 90      and     a + b + c = 20

Square the second equation, subtract it from the first equation, then simplify.

Square the second equation:

(a + b + c)² = 20²

a² + b² + c² + 2ab + 2bc + 2ac = 400

Subtract the equations:

   a² + b² + c² + 2ab + 2bc + 2ac = 400

- (<u>a² + b² + c²                                 </u> = <u>90</u>)

                         2ab + 2bc + 2ac = 310

Simplify:

2(ab + bc + ac) = 310

<u>÷2                     </u>  <u>÷2    </u>

  ab + bc + ac = 155

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