MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Algebraic Identities

If x +2p+3q...

Question

If $x + 2 p + 3 q = 14$ and $2 x p + 6 p q + 3 q x = 4$ , find the value of $x^{2} + 4 p^{2} + 9 q^{2} .$

A

199

No worries! We‘ve got your back. Try BYJU‘S free classes today!

B

132

No worries! We‘ve got your back. Try BYJU‘S free classes today!

C

188

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

D

178

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $188$
Given,
$x + 2 p + 3 q = 14$ and $2 x p + 6 p q + 3 q x = 4$
We know,
$(a + b + c)^{2} = (a^{2} + b^{2} + c^{2}) + 2 (a b + b c + c a)$
Here,
$a = x, b = 2 p, c = 3 q$
Thus,
$(x + 2 p + 3 q)^{2} = x^{2} + 4 p^{2} + 9 q^{2} + 2 (2 x p + 6 p q + 3 q x)$
$=> 14^{2} = x^{2} + 4 p^{2} + 9 q^{2} + 2 (4)$
$=> 196 - 8 = x^{2} + 4 p^{2} + 9 q^{2}$
$=> x^{2} + 4 p^{2} + 9 q^{2} = 188$

Suggest Corrections

thumbs-up

2

Similar questions

x = \frac{\sqrt{2 p + 3 q} + \sqrt{2 p - 3 q}}{\sqrt{2 p + 3 q} - \sqrt{2 p - 3 q}}

, find the value of

3 q x^{2} - 4 p x + 3 q

x = \frac{6 p q}{p + q}

\frac{x + 3 p}{x - 3 p} + \frac{x + 3 q}{x - 3 q}

x = \frac{6 p q}{p + q}

then find value of

\frac{x + 3 p}{x - 3 p} + \frac{x + 3 q}{x - 3 q}

State whether the following statement is true or false:

{(2 p - 3 q)}^{2}

4 p^{2} + 9 q^{2} - 12 p q

2 p + 3 q = 18

4 p^{2} + 4 p q - 3 q^{2} - 36 = 0

(2 p + q)

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Algebraic Identities

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Algebraic Identities

Standard X Mathematics

Join BYJU'S Learning Program

CrossIcon