addinbernier
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Show all work to solve the equation for x. If a solution is extraneous, be sure to identify it in your final answer.

[tex]\sqrt{x+7} -1=x\\[/tex]

Sagot :

Answer:

x = 2 and x = -3

Step-by-step explanation:

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

[tex]\sqrt{x+7} -1=x[/tex]

Adding 1 to both sides,

[tex]\sqrt{x+7} -1+1=x+1\\\\\sqrt{x+7}=x+1[/tex]

Squaring both sides,

[tex]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[/tex]

Hence, this is the required solution.

[tex]\bf\huge x=2 [/tex]

Step-by-step explanation:

Given that :

  • [tex]\sqrt{x+7} -1=x\\[/tex]

to find :

  • [tex]\sqrt{x+7} -1=x\\[/tex]

explanation :

⟼ [tex]\sqrt{x+7} -1=x\\[/tex]

⟼ √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

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

Therefore,

⟼ x = 2.

verification :

⟼ let take x = 2

⟼ [tex]\sqrt{x+7} -1=x\\[/tex]

⟼ √2+7 - 1 = 2

⟼ √9 - 1 = 2

⟼ 3 - 1 = 2

⟼ 2 = 2

hence verified ☑️

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