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AP TET Paper 2 Math and Science Model Paper 4

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Question : 94 of 150

Marks: +1, -0

If

x + y = 7

x^{2} + y^{2} = 25

, then the value of

\left(\frac{1}{x}+\frac{1}{y}\right)

is:

$\frac{12}{7}$
$\frac{7}{25}$
$\frac{7}{12}$
$\frac{1}{10}$

Solution:

Concept:

Use the identity

(x + y)^2 = x^2 + y^2 + 2xy

to find

xy

, then express

\frac{1}{x} + \frac{1}{y}

as

\frac{x+y}{xy}

.

Explanation:

Given:

x + y = 7

and

x^2 + y^2 = 25

.

Square both sides of

x + y = 7

.

(x + y)^2 = 7^2 = 49

Using the identity:

x^2 + y^2 + 2xy = 49

Substitute

x^2 + y^2 = 25

:

25 + 2xy = 49

So,

2xy = 24

, hence

xy = 12

.

Now,

\frac{1}{x} + \frac{1}{y} = \frac{x + y}{xy} = \frac{7}{12}

.

Answer:

\frac{1}{x} + \frac{1}{y} = \frac{7}{12}

Correct option: C.

\frac{7}{12}

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