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Sagot :
Answer:
Step-by-step explanation:
(13-2w)^2 = 169 - 52w + 4w^2
(w+6)^2 = w^2 + 12w + 36
Setting them equal:
169 - 52w + 4w^2 = w^2 + 12w + 36
3w^2 - 64w + 133 = 0
Using the quadratic formula, we get
x = (64 +/- sqrt(64^2 - 4*3*133))/6
64^2-12*133 = 2500. sqrt(2500) = 50.
x = (64 +/- 50)/6.
x = 19 or 14/6 = 7/3.
Solving the original equation:
7 = 3w.
w = 7/3.
Therefore 19 is extraneous.
x = 19 is the extraneous solution Li Juan obtained.
The given equation is 13 - 2w = w + 6.
We need to solve the equation by squaring both sides of the equation.
What is an equation?
In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Now, 13 - 2w = w + 6 squaring both sides of the equation.
That is, (13-2w)²= 169 - 52w + 4w²
(w+6)²= w²+ 12w + 36
Setting them equal, we get
169 - 52w + 4w² = w² + 12w + 36
⇒3w²- 64w + 133 = 0
Now, using the quadratic formula, we get
x = (64±√(64² - 4×3×133))/6
⇒x = (64±√2500)/6.
⇒x = (64±√50)/6.
⇒x = 19 or 14/6 = 7/3.
Solving the original equation, we get
7 = 3w⇒w = 7/3
Therefore, x = 19 is the extraneous solution Li Juan obtained.
To learn more about an equation visit:
https://brainly.com/question/1529522.
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