Question

(4x+1)²+(2x+3)²/4x²+12x+9=61/36 Solve the equation.

Answer 1

Answer:

x = 0.643 or x = 0.617.

Step-by-step explanation:

Given equation is

$\rm \dfrac{(4x+1)^2+(2x+3)^2}{4x^2+12x+9} = \dfrac{61}{36}$

On solving,

$\rm \dfrac{(4x+1)^2+(2x+3)^2}{4x^2+12x+9} = \dfrac{61}{36}\\\dfrac{16x^2+1+8x+4x^2+9+12x}{4x^2+12x+9} = \dfrac{61}{36}\\\dfrac{20x^2+20x+10}{4x^2+12x+9} = \dfrac{61}{36}\\36\times (20x^2+20x+10)=61\times (4x^2+12x+9)\\720x^2+720x+360=244x^2+732x+549\\(720-244)x^2+(720-732)x+360-549=0\\476x^2-12x-189=0\\\\\text{ On solving this quadratic equation,}\\x=\dfrac{-(-12)\pm \sqrt{(-12)^2-4\cdot (476)\cdot (-189)}}{2\times 476}=\dfrac{12\pm 600}{952}\\\Rightarrow x=0.643\ \ \ \ or\ \ \ \ \ \ x=-0.617$