If a + b + c = 0 and $a^2 + b^2 + c^2 =

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Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Algebra

Question:

If a + b + c = 0 and $a^2 + b^2 + c^2 = 40 $, then what is the value of 4ab + 4bc + 4ca ?

Options:

-40

-20

-160

-80

Correct Answer:

-80

Explanation:

If a + b + c = 0

$a^2 + b^2 + c^2 = 40 $

what is the value of 4ab + 4bc + 4ca

( a + b + c )² = ( a² + b² + c² + 2(ab + bc + ca))

0 = 40 + 2(ab + bc + ca)

2(ab + bc + ca) = -40

4ab + 4bc + 4ca = 2 (2ab + 2bc + 2ca) = 2 × -40 = 80