When solved correctly, the equation 4x−8−−−−−√=x−5 has solutions of x=3 and x=11.
1 answer:
Answer:
x = 3 is extraneous
Step-by-step explanation:
Given
= x - 5 ( square both sides to clear the radical )
4x - 8 = (x - 5)² ← expand using FOIL
4x - 8 = x² - 10x + 25 ( subtract 4x - 8 from both sides )
0 = x² - 14x + 33 ← in standard form
0 = (x - 11)(x - 3) ← in factored form
Equate each factor to zero and solve for x
x - 11 = 0 ⇒ x = 11
x - 3 = 0 ⇒ x = 3
As a check
Substitute these values into the equation and if both sides are equal then they are solutions
x = 11
left side = =
= 6
right side = 11 - 5 = 6
Thus x = 11 is a solution
x = 3
left side = =
= 2
right side = 3 - 5 = - 2 ≠ 2
Thus x = 3 is an extraneous solution
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Description:
This will be no solution because when we add 10 to both sides of the equation then simplify it. After that we will subtract 6 from both sides. It will give us no solution. For more info please see the attachment.
Answer: No solution
Hope this helps.
