Israel started to solve a radical equation in this way:
square root of x plus 6 β 4 = x
squar...
Mathematics, 04.09.2020 09:01 chimwim8347
Israel started to solve a radical equation in this way:
square root of x plus 6 β 4 = x
square root of x plus 6 β 4 + 4 = x + 4
square root of x plus 6 = x + 4
(square root of x plus 6)2 = (x + 4)2
x + 6 = x2 + 8x + 16
x + 6 β 6 = x2 + 8x + 16 β 6
x = x2 + 8x + 10
x β x = x2 + 8x + 10 β x
0 = x2 + 7x + 10
0 = (x + 2)(x + 5)
x + 2 = 0 x + 5 = 0
x + 2 β 2 = 0 β 2 x + 5 β 5 = 0 β 5
x = β2 x = β5
Solutions = β2, β5
What error did Israel make?
He subtracted 6 before subtracting x.
He added 4 before squaring both sides.
He factored x2 + 7x + 10 incorrectly.
He did not check for extraneous solutions.
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