Question

Can someone help me solve pleaseFormula1" title="x + 2 \sqrt{x} - 3 = 0" alt="x + 2 \sqrt{x} - 3 = 0" align="absmiddle" class="latex-formula">
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Answer 1

Answer:

x = 1

Step-by-step explanation:

Given

x + 2$\sqrt{x}$ - 3 = 0 ( subtract x - 3 from both sides )

2$\sqrt{x}$ = 3 - x ( square both sides )

4x = (3 - x)² ← expand using FOIL

4x = 9 - 6x + x² ( subtract 4x from both sides )

0 = x² - 10x + 9 ← in standard form

0 = (x - 1)(x - 9) ← in factored form

Equate each factor to zero and solve for x

x - 1 = 0 ⇒ x = 1

x - 9 = 0 ⇒ x = 9

As a check

Substitute these values into the left side of the equation and if equal to the right side then they are solutions.

x = 1 : 1 + 2$\sqrt{1}$ - 3 = 1 + 2 - 3 = 0 → x = 1 is a solution

x = 9 : 9 + 2$\sqrt{9}$ - 3 = 9 + 6 - 3 = 12 ≠ 0

x = 9 is an extraneous solution while x = 1 is a solution

Answer 2

x + 2√x - 3 = 0

x = 1

Must click thanks and mark brainliest