Value of Polynomial

Algebra Level 1

If $3a+4b=\frac{3}{x},$ what is the value of $27a^2x^2+72abx^2+48b^2x^2?$

24 26 27 25

2 solutions

Sanjeev Prasad
Feb 28, 2014

3a + 4b =3/x

squaring both side;

(3a +4b)^2 =(3/x)^2

9a^2 +16b^2 +24ab =9/x^2

multiplying with 3 on both sides and cross- multiplying 'x' square

27a^2 +48b^2 + 72ab =27/x^2

hence L .H . S. =27

Mohd Naim Mohd Amin
May 24, 2014

Hello,

as x = 3 / (3a + 4b) ----> by squaring both sides,

x^2 = 9 / (3a + 4b)^2

3x^2(9a^2 + 24ab + 16b^2) = 3[ 9 / (3a + 4b) ]^2 x [( 3a + 4b)^2]

= 3(9)

=27

thanks.....