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Misaka solved the radical equation x – 3 = square root of 4x-7 but did not check her solutions. (x – 3)2 = square root of 4x-7^2 x2 – 6x + 9 = 4x – 7 x2 – 10x + 16 = 0 (x – 2)(x – 8) = 0 x = 2 and x = 8 Which shows the true solution(s) to the radical equation x – 3 = square root of 4x-7 x = 2 x = 8 x = 2 and x = 8 There are no true solutions to the equation.

User Avraham
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1 Answer

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Answer:

x=8 is a true solution of the radical equation

Explanation:

we have


x-3=√(4x-7)

Solve for x

squared both sides


(x-3)^(2)=4x-7\\\\x^(2)-6x+9=4x-7\\\\ x^(2)-10x+16=0

Convert to factored form


x^(2)-10x+16=(x-2)(x-8)

The solutions are x=2 and x=8

Verify the solutions

For x=2

Substitute in the original equation


2-3=√(4(2)-7)


-1=1 ----> is not true

therefore

x=2 is not a true solution of the radical equation

For x=8

Substitute in the original equation


8-3=√(4(8)-7)


5=5 ----> is true

therefore

x=8 is a true solution of the radical equation

User Alexandrius
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