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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The length of the other two sides is 10 and 35 respectively.
<h3>What is a ratio?</h3>A ratio is a quantitative relation showing the comparison between two or more numbers. It can also be written in the fractional form where the first part is the numerator and the second part is called the denominator.
From the given information:
- The sides of the triangle = 2:7:8
- The total sides of the triangle = 2+7+8 = 17
We are being told that the longest side is the triangle is equal to 40.
i.e.
x = 85
Now for the other two sides 2 and 7, their length is as follows.
Therefore, we can conclude that the length of the other two sides is 10 and 35 respectively.
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