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Question 11 of 25
What is the solution to the equation below?
X+ 4 = V8 - x
O A. x = 0
B. X = -7
C. X = -1
D. X= 4

Question 11 Of 25 What Is The Solution To The Equation Below X 4 V8 X O A X 0 B X 7 C X 1 D X 4 class=

Sagot :

[tex]\\ \sf\longmapsto x+4=\sqrt{8-x}[/tex]

[tex]\\ \sf\longmapsto (x+4)^2=8-x[/tex]

[tex]\\ \sf\longmapsto x^2+16+8x=8-x[/tex]

[tex]\\ \sf\longmapsto x^2+8x-x+16-8=0[/tex]

[tex]\\ \sf\longmapsto x^2+7x+8=0[/tex]

[tex]\\ \sf\longmapsto x^2-8x+x+8[/tex]

[tex]\\ \sf\longmapsto (x-8)(x-1)=0[/tex]

[tex]\\ \sf\longmapsto x=8,-1[/tex]

Option C

Answer:

[tex]{ \rm{x + 4 = \sqrt{8 - x} }} \\ \\ { \rm{ {(x + 4)}^{2} = {( \sqrt{8 - x}) }^{2} }} \\ \\ { \rm{(x + 4)(x + 4) = 8 - x}} \\ \\ { \rm{ {x}^{2} + 8x + 16 = 8 - x}} \\ \\ { \rm{ {x}^{2} + 9x + 8 = 0 }} \\ \\ { \rm{(x + 1)(x + 8) = 0}} \\ \\ { \boxed{ \tt{x _{1} = {}^{ - } 1}}} \: \: { \rm{and}} \: \: { \boxed{ \tt{x _{2} = {}^{ - } 8}}}[/tex]

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