Count the solutions
x 2 + 1 9 − 2 x = 1
How many solutions does the above equation has?
The answer is 1.
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2 solutions
Is your arguement always correct? In that case according to you x 3 = 2 x 2 should have 3 solutions because the highest degree of the variable is 3 , but the solutions are 2 namely x = 2 and x = 0 .
The fact is: the number of solutions are less than or equal to the highest degree of the variable. So the solutions can be 1 or 0 . You can't simply say that there is only 1 solution.
x 2 + 1 9 − 2 x = 1
⇒ 2 + 1 9 − 2 x = x
⇒ 1 9 − 2 x = x − 2
⇒ ( 1 9 − 2 x ) 2 = ( x − 2 ) 2 ; [ Square on both sides ]
⇒ 1 9 − 2 x = x 2 − 4 x + 4
After solving it, we get x = 5 and x = − 3
After verifying, we get x = − 3
Hence the equation have only 1 solution
Remove the square root in 4th step.
The highest degree of the variable is 1 so there is only one solution