(D) For equation $I$:$\frac{9}{\sqrt{x}} + \frac{19}{\sqrt{x}} = \sqrt{x}$$\frac{9+19}{\sqrt{x}} = \sqrt{x}$$28 = \sqrt{x} \times \sqrt{x}$$x = 28$For

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if $x = y$ or relationship between $x$ and $y$ cannot be established.

(D) For equation $I$:$\frac{9}{\sqrt{x}} + \frac{19}{\sqrt{x}} = \sqrt{x}$$\frac{9+19}{\sqrt{x}} = \sqrt{x}$$28 = \sqrt{x} \times \sqrt{x}$$x = 28$For equation $II$:$y^{5} = \frac{(28)^{11/2}}{\sqrt{y}}$$y^{5} \times y^{1/2} = (28)^{11/2}$$y^{5 + 1/2} = (28)^{11/2}$$y^{11/2} = (28)^{11/2}$$y = 28$Comparing the values,$x = 28$ and $y = 28$,therefore $x = y$.

Competitive Quantitative Aptitude Algebra QUADRATIC EQUATION

Medium

Solve the given two equations and select the correct answer from the given options.
$I.$ $\frac{9}{\sqrt{x}} + \frac{19}{\sqrt{x}} = \sqrt{x}$
$II.$ $y^{5} - \frac{(2 \times 14)^{11/2}}{\sqrt{y}} = 0$

A
if $x > y$
B
if $x < y$
C
if $x \ge y$
D
if $x = y$ or relationship between $x$ and $y$ cannot be established.

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Algebra

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QUADRATIC EQUATION

The value of $k$ for which the quadratic equation $(k + 11)x^2 - (k + 3)x + 1 = 0$ has real and equal roots is:

Easy

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Solve the given two equations and select the correct option.
$I.$ $36 x^{2}+47 \sqrt{7} x+105=0$
$II.$ $35 y^{2}+20 \sqrt{3} y+63 \sqrt{2} y+36 \sqrt{6}=0$

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If $a, b, c$ are in $G.P.$,then the equations $ax^2 + 2bx + c = 0$ and $dx^2 + 2ex + f = 0$ have a common root if $\frac{d}{a}, \frac{e}{b}, \frac{f}{c}$ are in

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Let $x = \frac{\sqrt{13} + \sqrt{11}}{\sqrt{13} - \sqrt{11}}$ and $y = \frac{1}{x}$. Then the value of $3x^2 - 5xy + 3y^2$ is:

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If $\lambda \in R$ is such that the sum of the cubes of the roots of the equation $x^2 + (2 - \lambda) x + (10 - \lambda) = 0$ is minimum,then the magnitude of the difference of the roots of this equation is

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Solve the given two equations and select the correct answer from the given options.$I.$ $\frac{9}{\sqrt{x}} + \frac{19}{\sqrt{x}} = \sqrt{x}$$II.$ $y^{5} - \frac{(2 \times 14)^{11/2}}{\sqrt{y}} = 0$

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The value of $k$ for which the quadratic equation $(k + 11)x^2 - (k + 3)x + 1 = 0$ has real and equal roots is:

Solve the given two equations and select the correct option.$I.$ $36 x^{2}+47 \sqrt{7} x+105=0$$II.$ $35 y^{2}+20 \sqrt{3} y+63 \sqrt{2} y+36 \sqrt{6}=0$

If $a, b, c$ are in $G.P.$,then the equations $ax^2 + 2bx + c = 0$ and $dx^2 + 2ex + f = 0$ have a common root if $\frac{d}{a}, \frac{e}{b}, \frac{f}{c}$ are in

Let $x = \frac{\sqrt{13} + \sqrt{11}}{\sqrt{13} - \sqrt{11}}$ and $y = \frac{1}{x}$. Then the value of $3x^2 - 5xy + 3y^2$ is:

If $\lambda \in R$ is such that the sum of the cubes of the roots of the equation $x^2 + (2 - \lambda) x + (10 - \lambda) = 0$ is minimum,then the magnitude of the difference of the roots of this equation is

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Solve the given two equations and select the correct answer from the given options.
$I.$ $\frac{9}{\sqrt{x}} + \frac{19}{\sqrt{x}} = \sqrt{x}$
$II.$ $y^{5} - \frac{(2 \times 14)^{11/2}}{\sqrt{y}} = 0$

Solve the given two equations and select the correct option.
$I.$ $36 x^{2}+47 \sqrt{7} x+105=0$
$II.$ $35 y^{2}+20 \sqrt{3} y+63 \sqrt{2} y+36 \sqrt{6}=0$