CAT 2024 Functions Question (Hard)

Question

Let , and be real numbers satisfying 4 left x 2 y 2 z 2 right a 4 x-y-z 3 a Then equals

Accepted Answer

Step 1 We are given 1. 2. We need to find . --- Step 2 First express from equation 2 x - y - z 4 We also have . We can try to express and in terms of . Alternatively, let s try squaring . Let k x - y - z 4 Then x - y - z k Now, let s compute . We can write x 2 y 2 z 2 We can express in terms of and

CAT 2024

Quantitative

Functions

Hard

Let $x, y$ , and $z$ be real numbers satisfying $\begin{aligned} & 4\left(x^2+y^2+z^2\right)=a \\ & 4(x-y-z)=3+a \end{aligned}$ Then $a$ equals

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