Answer:
1. x = 12
2. 3∛4 feet.
Step-by-step explanation:
1. We are given the equation of x as [tex]\sqrt{x - 3} + x = 9[/tex] and we have to find the extraneous solution of the equation.
Now, [tex]\sqrt{x - 3} + x = 9[/tex] ............. (1)
⇒ [tex]\sqrt{x - 3} = 9 - x[/tex]
Squaring both sides we get,
⇒ x - 3 = 81 - 18x + x²
⇒ x² - 19x + 84 = 0
⇒ x² - 12x - 7x + 84 = 0
⇒ (x - 12)(x - 7) = 0
⇒ x = 12 or 7.
Now, putting x = 12 in the equation (1) we get,
[tex]\sqrt{12 - 3} + 12 \neq 9[/tex]
Again, putting x = 7 in the equation (1) we get,
[tex]\sqrt{7 - 3} + 7 = 9[/tex]
Therefore, x = 12 is an extraneous solution of this equation. (Answer)
2. The volume of a cube with side lengths a ft. is given to be 108 ft³.
So, a³ = 108
⇒ a = 3∛4 feet.
Therefore, the length of the sides of the cube are each 3∛4 feet. (Answer)
