Question

√x + 8/√x = 6
solve the question​

Answer 1

Step-by-step explanation:

Consider,L.H.S.= root x + 8/ root x

& R.H.S. = 6

Now,square both sides

(root x + 8/ root x )^2 = 6^2

we can see identity (a + b)^2=a^2 + b^2 + 2ab on L.H.S.

=> (root x )^2 + ( 8 / root x )^2 + 2 × root x × 8 / root x = 36

=> x + 64/x + 16 = 36

=> x + 64/x -20 = 0

NOW TAKE L.C.M

=> (x^2 + 64 - 20x )/ x = 0

=> x^2 + 64 - 20x = 0

Now,D(Discriminant) = b^2 - 4ac

Here, a = 1, b = -20 , c = 64(Supposed from general form of quadratic equation i.e. ax^× + bx + c)

therefore,D = (-20)^2 - 4(1)(64) = 400 - 256 = 144

we know, x = -b +/- root D ÷ 2a(QUADRATIC FORMULA)

=> x = -(-20) + root 144 ÷ 2(1) or -(-20) - root 144 ÷ 2(1)

=> x = 20 + 12 ÷ 2 or 20 - 12 ÷ 2

=> x = 32÷2 or 8 ÷ 2

Therefore, x = 16 or 4 ans.