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Question 56
If $$x, y, z$$ are three integers such that $$x + y = 8, y + z = 13$$ and $$z + x = 17$$, then the value of $$\frac{x^2}{yz}$$ is:
Solution
x + y = 8 ----(1)
y + z = 13Â ----(2)
z + x = 17Â ----(3)
Eq (1) + (2) + (3),
2(x + y + z) = 8 + 13 +Â 17
x + y + z = 38/2 = 19 ----(4)
From eq (3) and (4),
x + 13 = 19
x = 6
From eq(3),
z + x = 17
z + 6 = 17
z = 11
From eq(2),
y + z = 13
y + 11 = 13
y = 2
$$\frac{x^2}{yz}$$
=Â $$\frac{6^2}{2 \times 11}$$
= 36/22 = 18/11
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