If $a^2 + b^2 + c^2 = 62 $ and a + b + c

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Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Algebra

Question:

If $a^2 + b^2 + c^2 = 62 $ and a + b + c = 12, then what is the value of $ 4ab + 4bc + 4ca $ ?

Options:

164

148

152

160

Correct Answer:

164

Explanation:

a²+ b² + c² = 62

a + b + c = 12

We know that,

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

12² = 62 + 2(ab + bc + ca)

144 = 62 + 2(ab + bc + ca)

82 = 2(ab + bc + ca)

41 = ab + bc + ca

4ab + 4bc + 4ca = 4 × 41 = 164