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andreev551 [17]
3 years ago
12

I don't remember what it is that I'm doing, as I did the lessons before spring break. Help?

Mathematics
1 answer:
blsea [12.9K]3 years ago
6 0
Extraneous solutions, is answers that we get because of squaring both sides of the radical equation, but in reality, they are not going to be the solutions of  the given equation.
(√(4x+41))²=(x+5)²
4x+41=x²+10x+25
x²+6x-16=0
(x-2)(x+8)=0
x1=2 , x2=-8,
And now we must to check them by substitution into initial equation

√(4x+41)=x+5
1)   x=2,   √(4*2+41)=2+5, √49=7, 7=7 true
2) x=-8,     √(4*(-8)+41)=-8+5,   √9 =-3    false,
so an extraneous solution x=-8
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