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SSC Selection Post 2022 PYQ — Question 51

SSC Selection Post - Matriculation Level - 3 Feb 2022 - Shift 1 • Quantitative Aptitude • Q51

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If x2 + y2 + z2 + 26 = 2 (4x + y + 3z), then find the value of x + y + z.

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Correct answer: A

Explanation

The correct answer is Option 1 i.e. 8.

⇒ x2 + y2 + z2 + 26 = 2 (4x + y + 3z)

⇒ x2 - 8x + y2 - 2y + z2 - 6y + 26 = 0

⇒ (x - 4)2 - 16 + (y - 1)2 - 1 + (z - 3)2 - 9 + 26 = 0

⇒ (x - 4)2 + (y - 1)2 + (z - 3)2 = 0

⇒ x - 4 = 0 ⇒ x = 4

⇒ y - 1 = 0 ⇒ y = 1

⇒ z - 3 = 0 ⇒ z = 3

⇒ x + y + z = 4 + 1 + 3 = 8