CAT 2002 Question Paper Question 28

Question 28

If $$x^2 + 5y^2 + z^2 = 2y(2x+z)$$, then which of the following statements is(are) necessarily true?

A. x = 2y B. x = 2z C. 2x = z


The equation is not satisfied for only x = 2y.

Using statements B and C, i.e., x = 2z and 2x = z, we see that the equation is not satisfied.

Using statements A and B, i.e., x = 2y and x = 2z, i.e., z = y = x/2, the equation is satisfied.

Option c) is the correct answer.

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Nidhi R

10 months, 3 weeks ago

It can also be solved in this way:-

x^2 + 5y^2 + z^2 = 2y (2x +z)
x^2 -4xy+ 4y^2 + z^2 +y^2 -2yz = 0
(x-2y)^2 + (y-z)^2 = 0

thus, x-2y=0 and y=z
so, x=2y=2z

Option (C) is the correct answer


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