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Question
If `[(xy, 4),(z + 6, x + y)] = [(8, w),(0, 6)]`, then find values of x, y, z and w.
Solution
Given that: `[(xy, 4),(z + 6, x + y)] = [(8, w),(0, 6)]`
Equating the corresponding elements,
xy = 8
w = 4
z + 6 = 0
⇒ z = – 6, x + y = 6
Now, solving x + y = 6 ......(i)
And xy = 8 .....(ii)
From equation (i), y = 6 – x ......(iii)
Putting the value of y in equation (ii) we get,
x(6 – x) = 8
⇒ 6x – x2 = 8
⇒ x2 – 6x + 8 = 0
⇒ x2 – 4x – 2x + 8 = 0
⇒ x(x – 4) – 2(x – 4) = 0
⇒ (x – 4) (x – 2) = 0
∴ x = 4, 2
From equation (iii)
y = 2, 4
Hence, x = 4 or 2, y = 2 or 4, z = – 6 and w = 4.
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