### Question 13

SSC-CGL 2020 Mar 3 Shift 1

Given x + y = 8, y + z = 13, z + x = 17, then the value of x²/yz = ?

### Solution in Short

Adding the three equations gives x + y + z = 19. Subtracting each of the given equations from this one, we get x = 6, y = 2 and z = 11. Finally, x²/yz = 18/11 ans!

### Solution in Detail

Write the given equations like this:

$\displaystyle x + y = 8\text{ . . . (1)}$

$\displaystyle y + z = 13\text{ . . . (2)}$

$\displaystyle z + x = 17\text{ . . . (3)}$

Adding all the three equations,

$\displaystyle 2x + 2y + 2z = 38$

$\displaystyle \implies x + y + z = 19 \text{. . . (4)}$

Equation (4) - (1) gives $\displaystyle z = 11$

Equation (4) - (2) gives $\displaystyle x = 6$

Equation (4) - (3) gives $\displaystyle y = 2$

$\displaystyle \therefore \frac{x^2}{yz} = \frac{6 \times 6}{2 \times 11} = \frac {18}{11}\:\underline{Ans}$

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