SSC CGL 2021 PYQ — Question 51

The correct answer is Option 2 i.e -36.

Here one can see that the numerator part can be further simplified as $[(3\sqrt2x)^3 + (2\sqrt3y)^3]$ and the denominator part can be simplified as $[3\sqrt2x + 2\sqrt3y]$

As one knows that [a³ + b³ = a² - ab + b²]

Now one has $\frac{[(3\sqrt2x)^3 + (2\sqrt3y)^3]}{3\sqrt2x + 2\sqrt3y}$

By using the above identity we get,

 $\Rightarrow \frac{[3\sqrt2x + 2\sqrt3y] \times [18x^2 + 12y^2 - 6\sqrt6xy]}{[3\sqrt2x + 2\sqrt3y]} = Ax^2 + By^2 + Cxy$

$\Rightarrow 18x^2 + 12y^2 - 6\sqrt6xy= Ax^2 + By^2 + Cxy$

On comparing L.H.S and R.H.S one gets

A = 18 and B = 12 and C = $-6\sqrt6$

Here one has to find the value of A² - (B²+ C²)

= 18² - ( 12² +( $-6\sqrt6$²))

= -36.