Question

root2x+8+rootx+5=7 quadratic equation ​

Answer 1

Answer:

Step-by-step explanation:Raise both sides to the second power

    (√2x+8)2 = (-√x+5+7)2

    After squaring  

    2x+8 = x+5+49-14√x+5 . Current equation  

    2x+8 = x+5+49-14√x+5

    Isolate radical on the left hand side

    14√x+5 = -2x-8+x+5+49

     Tidy up  

    14√x+5 = -x+46. (14√x+5)2 = (-x+46)2

    After squaring  

    196x+980 = x2-92x+2116. x2  - 288x  + 1136 = 0

    This equation has two rational roots:

      {x1, x2}={284, 4}

Answer 2

√(2x+8)+√(x+5)=7

√(2x++8)=-√(x+5) +7

(√2x+8)^2=(-√x+5 +7)^2

2x+8=x+5+49-14√x+5

14√x+5=-2x-8+x+5+49

14√x+5=-x+46

(14√x+5)^2=(-x+46)^2

196x+980=x^2-92x+2116

x^2-288+1136=0

This equation has two rational roots

x=284,4

putting in main equation

√2x+8=-√x+5 +7

√2*(284)+8=-√(284)+5+7

24 is not equal to -10

Now,

√2x+8=-√x+5+7

√2*4+8=-√4+5+7

√16=4

so, x=4