Question

Find value of x. Chapter quadratic polynomial

Answer 1

Step-by-step explanation:

$\frac{ x }{ x+1 } + \frac{ x+1 }{ x } = \frac{ 34 }{ 15 }$

solve-

$15xx+\left(15x+15\right)\left(x+1\right)=34x\left(x+1\right)$

$15x^{2}+\left(15x+15\right)\left(x+1\right)=34x\left(x+1\right)$

$15x^{2}+15x^{2}+30x+15=34x\left(x+1\right)$

$30x^{2}+30x+15=34x\left(x+1\right)$

$30x^{2}+30x+15=34x^{2}+34x$

$30x^{2}+30x+15-34x^{2}=34x$

$-4x^{2}+30x+15=34x$

$-4x^{2}+30x+15-34x=0$

$-4x^{2}-4x+15=0$

$\left(-4x^{2}+6x\right)+\left(-10x+15\right)$

$2x\left(-2x+3\right)+5\left(-2x+3\right)$

$\left(-2x+3\right)\left(2x+5\right)$

$x=\frac{3}{2} x=-\frac{5}{2}$

Answer 2

Answer:

x = -5/2 , 3/2

Step-by-step explanation:

x/x+1 + x+1/x = 34/15

=>x^2+x^2+2x+1/x^2+x = 34/15

=>(2x^2+2x+1)15 = 34(x^2+x)

=>30x^2+30x+15 = 34x^2+34x

=>4x^2+4x-15 = 0

=>4x^2+10x-6x-15 = 0

=>2x(2x+5)-3(2x+5)=0

=>(2x+5) (2x-3) = 0

Hence, x = -5/2 and 3/2