(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

If $\alpha$ and $\beta$ are the roots of $ax^2 + bx + c = 0$,then the equation whose roots are $2 + \alpha$ and $2 + \beta$ is:

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Let $\alpha$ and $\beta$ be two distinct roots of the equation $x^3 + 3x^2 - 1 = 0$. The equation which has $(\alpha \beta)$ as its root is equal to

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The values of $a$ for which one root of the equation $x^2 - (a + 1)x + a^2 + a - 8 = 0$ exceeds $2$ and the other is lesser than $2$,are given by

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Solve the given two equations and select the correct option.
$I.$ $676 x^{2}-1=0$
$II.$ $y=\frac{1}{\sqrt[3]{13824}}$

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If $a + b + c = 0$,$a \neq 0$,$a, b, c \in Q$,then both the roots of the equation $ax^2 + bx + c = 0$ are

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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.$ $y^{5} - \frac{(2 \times 14)^{11/2}}{\sqrt{y}} = 0$

Similar Questions

If $\alpha$ and $\beta$ are the roots of $ax^2 + bx + c = 0$,then the equation whose roots are $2 + \alpha$ and $2 + \beta$ is:

Let $\alpha$ and $\beta$ be two distinct roots of the equation $x^3 + 3x^2 - 1 = 0$. The equation which has $(\alpha \beta)$ as its root is equal to

The values of $a$ for which one root of the equation $x^2 - (a + 1)x + a^2 + a - 8 = 0$ exceeds $2$ and the other is lesser than $2$,are given by

Solve the given two equations and select the correct option.$I.$ $676 x^{2}-1=0$$II.$ $y=\frac{1}{\sqrt[3]{13824}}$

If $a + b + c = 0$,$a \neq 0$,$a, b, c \in Q$,then both the roots of the equation $ax^2 + bx + c = 0$ are

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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.
$I.$ $676 x^{2}-1=0$
$II.$ $y=\frac{1}{\sqrt[3]{13824}}$