A If xy-yx- then x-yx-y is equal to-b If x-y-6-5 then x2-y2-x2-y2 is- -4 MARKS-

Application: 2 Marks Each a) x^y = y^x x = y^x/y (x/y)^x/y = x^x/y/y^x/y = x^x/y/x = x^x/y 1 b) x/y = 6/5 Let x = 6k, y = 5k x^2 + y^2/x^2 y^2 = (6k) ...

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Byju's Answer

Standard VII

Mathematics

Comparision of Quantities Using Exponents

a If xy=yx, t...

Question

a) If $x^{y} = y^{x},$ then $(\frac{x}{y})^{\frac{x}{y}}$ is equal to:

b) If $\frac{x}{y} = \frac{6}{5}$ then $\frac{x^{2} + y^{2}}{x^{2} - y^{2}}$ is: [4 MARKS]

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Solution

Application: 2 Marks Each

$a) x^{y} = y^{x}$

$x = y^{\frac{x}{y}}$

$(\frac{x}{y})^{\frac{x}{y}} = \frac{x^{\frac{x}{y}}}{y^{\frac{x}{y}}}$

$= \frac{x^{\frac{x}{y}}}{x}$

$= x^{\frac{x}{y} - 1}$

$b) \frac{x}{y} = \frac{6}{5}$

$L e t x = 6 k, y = 5 k$

$\frac{x^{2} + y^{2}}{x^{2} - y^{2}} = \frac{(6 k)^{2} + (5 k)^{2}}{(6 k)^{2} - (5 k)^{2}}$

$= \frac{61 k^{2}}{11 k^{2}}$

$= \frac{61}{11}$

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Similar questions

Q. a) If

x^{y} = y^{x},

then

(\frac{x}{y})^{\frac{x}{y}}

is equal to:

b) If

\frac{x}{y} = \frac{6}{5}

then

\frac{x^{2} + y^{2}}{x^{2} - y^{2}}

is:

Q. If

x, y

satisfy the equation

y^{x} = x^{y}

and

x = 2 y

, then

x^{2} + y^{2} = r

, the value of

\frac{r}{4}

Q. State whether True or False.
The H.C.F. and L.C.M. of:

x^{2} - y^{2}

and

x^{2} - x y

x - y; x (x + y) (x - y)

If true then enter

1

and if false then enter

0

Q. Assertion :Let a solution

y = y (x)

of the differential equation

x \sqrt{x^{2} - 1} d y - y \sqrt{y^{2} - 1} d x = 0

satisfy

y (2) = 2 / \sqrt{3}

y (x) = sec ({sec}^{- 1} x - \frac{π}{6})

Reason:

y (x)

is given by

\frac{1}{y} = \frac{2 \sqrt{3}}{x} - \sqrt{1 - \frac{1}{x^{2}}}

Q. If

\frac{d y}{d x} = \frac{x y}{x^{2} + y^{2}}; y (1) = 1;

then a value of

x

satisfying

y (x) = e

is:

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a) If xy=yx, then (xy)xy is equal to: b) If xy=65 then x2+y2x2−y2 is: [4 MARKS]

Application: 2 Marks Each a)xy=yx x=yxy (xy)xy=xxyyxy =xxyx =xxy−1 b)xy=65 Let x=6k,y=5k x2+y2x2−y2=(6k)2+(5k)2(6k)2−(5k)2 =61k211k2 =6111

a) If $x^{y} = y^{x},$ then $(\frac{x}{y})^{\frac{x}{y}}$ is equal to:

b) If $\frac{x}{y} = \frac{6}{5}$ then $\frac{x^{2} + y^{2}}{x^{2} - y^{2}}$ is: [4 MARKS]