Solve: √x+1 + √2x - 5 = 3......and the root is on both root x+1 and root 2x-5
Answers
Given: The equation √(x+1) + √(2x - 5) = 3
To find: The value of x?
Solution:
- Now we have given the expression as:
√(x+1) + √(2x - 5) = 3
√(x+1) = 3 - √(2x - 5)
- Now squaring on both sides, we get:
x + 1 = ( 3 - √(2x - 5) )^2
x + 1 = 9 + 2x - 5 - 6√(2x - 5)
6√(2x - 5) = 9 + 2x - 5 - x - 1
6√(2x - 5) = 3 + x
- Now again squaring on both sides, we get:
36(2x - 5) = (x + 3)^2
72x - 180 = x^2 + 9 + 6x
x^2 - 66x + 189 = 0
x^2 - 63x - 3x + 189 = 0
x(x-63) - 3(x-63) = 0
(x - 3)(x-63) = 0
x = 3,63
Answer:
So the value of x is 3 or 63.
Answer :
3 or 63
Given: The equation √(x+1) + √(2x - 5) = 3
To find: The value of x?
Solution:
Now we have given the expression as:
√(x+1) + √(2x - 5) = 3
√(x+1) = 3 - √(2x - 5)
Now squaring on both sides, we get:
x + 1 = ( 3 - √(2x - 5) )^2
x + 1 = 9 + 2x - 5 - 6√(2x - 5)
6√(2x - 5) = 9 + 2x - 5 - x - 1
6√(2x - 5) = 3 + x
Now again squaring on both sides, we get:
36(2x - 5) = (x + 3)^2
72x - 180 = x^2 + 9 + 6x
x^2 - 66x + 189 = 0
x^2 - 63x - 3x + 189 = 0
x(x-63) - 3(x-63) = 0
(x - 3)(x-63) = 0
x = 3,63
Answer:
So the value of x is 3 or 63.