Option D: [tex]x=-2[/tex] or [tex]x=-3[/tex]
Step-by-step explanation:
To solve the equation [tex]\sqrt{10-13x} =x-4[/tex]
To remove the square root, let us square on both sides of the equation, we get,
[tex](\sqrt{10-13x})^{2} =(x-4)^{2}[/tex]
Square root gets cancelled and expanding the term [tex](x-4)^{2}[/tex] , we get,
[tex]10-13x=x^{2} -8x+16[/tex]
Adding 13x to both sides,
[tex]10=x^{2} +5x+16[/tex]
Subtracting 10 from both sides, we get,
[tex]0=x^{2} +5x+6[/tex]
Solving this equation, we get,
[tex]0=(x+2)(x+3)[/tex]
Thus, [tex]x=-2[/tex] or [tex]x=-3[/tex]
Hence, the correct option is D.
A. [tex]x=2[/tex] or [tex]x=3[/tex]
Solving the equation results in [tex]x=-2[/tex] or [tex]x=-3[/tex]
Thus, [tex]x=2[/tex] or [tex]x=3[/tex] cannot be a solution to the equation [tex]\sqrt{10-13x} =x-4[/tex]
Thus, Option A is not a correct answer.
B. [tex]x=-6[/tex] or [tex]x=1[/tex]
Solving the equation results in [tex]x=-2[/tex] or [tex]x=-3[/tex]
Thus, [tex]x=-6[/tex] or [tex]x=1[/tex] cannot be a solution to the equation [tex]\sqrt{10-13x} =x-4[/tex]
Thus, Option B is not a correct answer.
C. No Solution
Solving the equation results in [tex]x=-2[/tex] or [tex]x=-3[/tex]
Hence, there exits a solution to the equation [tex]\sqrt{10-13x} =x-4[/tex]
Thus, Option C is not a correct answer.
Answer:
No solution
Step-by-step explanation:
Did the test and got 100%, dont listen to the other guy.
