# Question #74b80

Aug 26, 2016

${\left(2 a + 3 b\right)}^{2} + {\left(2 b - a\right)}^{2} = 49$, or,

$5 {a}^{2} + 8 a b + 13 {b}^{2} = 49$..

#### Explanation:

I will not give the complete Soln., but, will outline of the Soln.

Given, $a = 2 \cos x - 3 \sin x , 7 , b = \cos x + 2 \sin x$

Solve these eqns. for $\cos x , \mathmr{and} , \sin x$ in terms of $a \mathmr{and} b$.

Then, use the Identity $: {\cos}^{2} x + {\sin}^{2} x = 1$, and the Result will be there!.
Enjoy Maths.!