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N76 [4]
3 years ago
11

Help ASAP!!! Please show all work!!!!!!!

Mathematics
2 answers:
Vsevolod [243]3 years ago
8 0

\bf\huge x=2

Step-by-step explanation:

<h2>Given that :</h2>

  • \sqrt{x+7} -1=x\\

<h2>to find :</h2>

  • \sqrt{x+7} -1=x\\

<h2>explanation :</h2>

⟼ \sqrt{x+7} -1=x\\

⟼ √x + 7 = x + 1

⟼ x + 7 = x² + 2x + 1

⟼ x + 7 - x² - 2x - 1 = 0

⟼ -x + 6 -x² = 0

⟼ x² + x - 6 = 0

⟼ (x-2) (x+3) = 0

⟼ x = 2 and x = -3

<h3>When x = -3 the original equation √x+7-1 = x does not hold true. We will drop x = -3 from the solution set. </h3>

Therefore,

⟼ x = 2.

<h2>verification :</h2>

⟼ let take x = 2

⟼ \sqrt{x+7} -1=x\\

⟼ √2+7 - 1 = 2

⟼ √9 - 1 = 2

⟼ 3 - 1 = 2

⟼ 2 = 2

<h2>hence verified ☑️</h2>
Anastaziya [24]3 years ago
6 0

Answer:

x = 2 and x = -3

Step-by-step explanation:

We need to find the value of x in the below expression.

\sqrt{x+7} -1=x

Adding 1 to both sides,

\sqrt{x+7} -1+1=x+1\\\\\sqrt{x+7}=x+1

Squaring both sides,

x+7=(x+1)^2\\\\x+7=x^2+1+2x\\\\x^2+1+2x-x-7=0\\\\x^2+x-6=0\\\\x=2\ and\ -3

Hence, this is the required solution.

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