I- 2 x 2-4-13 x -2 -13-0II- 10 y 2-18-5 -13 y -9 -13-0A- x - yB- x - y or relationship cannot be establishedC- xy E- x - y

The correct option is A x ≥ yEquation I 2x^2 (4+√(13))x+2√(13)=0 ⇒ 2x(x 2) √(13)(x 2)=0 ⇒ (x 2)(2x √(13))=0 ∴ x=2, √(13)/2 Equation II 10y^2 (18+5√(13))y+9√(13 ...

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Quantitative Aptitude

Equations

I. 2 x 2-4+√1...

Question

$I . 2 x^{2} - (4 + \sqrt{13}) x + 2 \sqrt{13} = 0$
$I I . 10 y^{2} - (18 + 5 \sqrt{13}) y + 9 \sqrt{13} = 0$

x > y

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x < y

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\leq

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x = y or relationship cannot be established

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Solution

The correct option is B x $\geq$ y
Equation I
$2 x^{2} - (4 + \sqrt{13}) x + 2 \sqrt{13} = 0$
$\Rightarrow 2 x (x - 2) - \sqrt{13} (x - 2) = 0$
$\Rightarrow (x - 2) (2 x - \sqrt{13}) = 0$
$∴ x = 2, \frac{\sqrt{13}}{2}$
Equation II
$10 y^{2} - (18 + 5 \sqrt{13}) y + 9 \sqrt{13} = 0$
$\Rightarrow 2 y (5 y - 9) - \sqrt{13} (5 y - 9) = 0$
$\Rightarrow (5 y - 9) (2 y - \sqrt{13}) = 0$
$∴ y = \frac{9}{5}, y = \frac{\sqrt{3}}{2}$
Hence, x $\geq$ y

Suggest Corrections

I. 2x2−(4+√13)x+2√13=0 II. 10y2−(18+5√13)y+9√13=0

The correct option is B x ≥ yEquation I 2x2−(4+√13)x+2√13=0 ⇒2x(x−2)−√13(x−2)=0 ⇒(x−2)(2x−√13)=0 ∴x=2,√132 Equation II 10y2−(18+5√13)y+9√13=0 ⇒2y(5y−9)−√13(5y−9)=0 ⇒(5y−9)(2y−√13)=0 ∴y=95,y=√32 Hence, x ≥ y

$I . 2 x^{2} - (4 + \sqrt{13}) x + 2 \sqrt{13} = 0$
$I I . 10 y^{2} - (18 + 5 \sqrt{13}) y + 9 \sqrt{13} = 0$