Question

Wich values of x satisfy this equation? Square root x^2 -10x+25+12square root x=15x? 1.425, 2.844, 16.15, 17.57

Answer 1

x = 17.57 satisfies the given equation

Solution:

Given equation is:

`√(x^2-10x+25) +12√(x) =15√(x)`

We have to find which values of x will satisfy the given equation

Thus means when we substitute the given value of x and solve the equation, both sides of equation must be same. i,e R.H.S = L.H.S

Substitute x = 1.425 in given equation

`√(1.425^2-10(1.425)+25) +12√(1.425) = 15√(1.425)\\\\√(2.030625-14.25+25)+14.3248=17.906\\\\√(12.780625) = 17.906-14.3248\\\\3.575 \\eq 3.5812`

Thus x = 1.425 does not satisfy the given equation

Substitute x = 2.844 in given equation

`√(2.844^2-10(2.844)+25) +12√(2.844) = 15√(2.844)\\\\√(8.088336-28.44 + 25) +20.236 = 25.296\\\\√(4.648336) +20.236 = 25.296\\\\2.156 + 20.236 = 25.296\\\\22.392\\eq 25.296`

Thus x = 2.844 does not satisfy the given equation

Substitute x = 16.15 in given equation

`√(16.15^2-10(16.15)+25) +12√(16.15) = 15√(16.15)\\\\√(260.8225 - 161.5 + 25) + 48.224} = 60.280\\\\√(124.3225) + 48.224 = 60.280\\\\ 59.374 \\eq 60.280`

Thus x = 16.15 does not satisfies the given equation

Substitute x = 17.57 in given equation

`√(17.57^2-10(17.57)+25) +12√(17.57) = 15√(17.57)\\\\12.57 + 50.2999 = 62.8\\\\62.8 = 62.8`

Thus x = 17.57 satisfies the given equation