Addinbernieridn
Answered

Join the IDNLearn.com community and start getting the answers you need today. Ask your questions and receive reliable, detailed answers from our dedicated community of experts.

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

We appreciate your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. Your questions deserve precise answers. Thank you for visiting IDNLearn.com, and see you again soon for more helpful information.