Question

If $3-3(x+2)=-10$ and $7(2y-3)=3+8y$, then the value of $3x^2-4xy+5y^2$ is

• A. $59$
• B. $49$
• C. $-40$
• D. $-50$

Answer 1

The correct option is A $59$

Given, $3-3(x+2)=-10$
$\Rightarrow 3-3x-6=-10$
$\Rightarrow -3x-3=-10$
$\Rightarrow -3x=-7$
$\Rightarrow x=\frac{7}{3}$

Also given, $7(2y-3)=3+8y$

$\Rightarrow 14y-21=3+8y$
$\Rightarrow 6y=24$
$\Rightarrow y=4$
Value of $3x^2-4xy+5y^2$ at $x=\frac{7}{3}$ and $y=4$ is

$3x^2-4xy+5y^2=$ $3{\left(\frac{7}{3}\right)}^2-4\left(\frac{7}{3}\right)\left(4\right)+5(4{)}^2$

$=3\left(\frac{49}{9}\right)-16\left(\frac{7}{3}\right)+80$

$=\frac{49}{3}-\frac{112}{3}+80$

$=\frac{49-112+240}{3}$

$=\frac{177}{3}$ $=59$

Hence, option A is correct.