CUET · MATHS · PYQ PAPER 2023
If \(\left[\begin{array}{c}x+y+z+w \\ x+y \\ x+z \\ x+w\end{array}\right]=\left[\begin{array}{c}10 \\ 6 \\ 5 \\ 3\end{array}\right]\), find the value of \(x^2+y^2-(w+z)^2\).
- A 16
- B 20
- C 4
- D 8
Answer & Solution
Correct Answer
(C) 4
Step-by-step Solution
Detailed explanation
\(x+y+z+w = 10\) \(x+y = 6\) \(x+z = 5\) \(x+w = 3\) \((x+y)+(z+w)=10 \Rightarrow 6+(z+w)=10 \Rightarrow z+w=4\) \(x+z+x+w = 5+3 \Rightarrow 2x+(z+w)=8 \Rightarrow 2x+4=8 \Rightarrow 2x=4 \Rightarrow x=2\) \(y=6-x = 6-2=4\) \(z=5-x = 5-2=3\) \(w=3-x = 3-2=1\)…
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