Question

find x if √(2x +1) +√(3x+4)=7​

Answer 1

Answer:

The value of $x$ are 480 and 4.

Step-by-step explanation:

we can expand the expression step by step.

$\sqrt{2x+1}+\sqrt{3x+4}=7$

Square on both sides of the equation,

$(\sqrt{2x+1}+\sqrt{3x+4}) ^2= 7^2\\\\(2x+1)+2(\sqrt{2x+1}\sqrt{3x+4})+3x+4=49\\\\5x+5+2(\sqrt{(2x+1)(3x+4)} =49\\\\5x+2(\sqrt{6x^2+8x+3x+4} )=49-5=44\\\\2(\sqrt{6x^2+8x+3x+4} )=44-5x$

Squaring on both sides again,

$\implies 4(6x^2+11x+4)=(44-5x)^2=1936-440x+25x^2\\\\\implies 24x^2+44x+16=25x^2-440x+1936\\\\\implies 25x^2-24x^2-440x-44x+1936-16=0\\\\\implies x^2-484x+1920=0$

Solving the quadratic equation, we obtain,

$x=\dfrac{484\pm\sqrt{484^2-4\times 1920}}{2}=\dfrac{484\pm476}{2}\\\implies x= \dfrac{484+476}{2}= \dfrac{960}{2}=480\ \ \ \ or \ \ \ x=\dfrac{484-476}{4}=4$

Hence the values of $x$ are 480 and 4.