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Virty [35]
1 year ago
15

2. √2x-5-√x+6=0(solving the following radical equations and check for extraneous solutions)

Mathematics
1 answer:
Norma-Jean [14]1 year ago
5 0

I assume the equation is

√(2x - 5) - √(x + 6) = 0

Note the domains for the root expressions:

• √(2x - 5) : 2x - 5 ≥ 0   ⇒   x ≥ 5/2

• √(x + 6) : x + 6 ≥ 0   ⇒   x ≥ -6

So any valid solution we find must be at least 5/2.

Move one term to the other side.

√(2x - 5) = √(x + 6)

Take squares.

(√(2x - 5))² = (√(x + 6))²

2x - 5 = x + 6

Solve for x :

x = 11

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f(x)=\left\{\begin{matrix}0.08x & x \leq 7500\\ 600+0.16(x-7500) & 7500 < x \leq 15000\\ 1800+0.20(x-15000) & 15000 < x\end{matrix}\right.

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