Question 86999This question is from textbook
: Find all real solutions to the equation.
the sqare root of x+4 minus 2 time the sqare root of x-1 = -1 This question is from textbook
You can put this solution on YOUR website! sqare root of x+4 minus 2 time the sqare root of x-1 = -1
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sqrt(x+4) - 2sqrt(x-1) = -1
sqrt(x+4) = 2sqrt(x-1)-1
Square both sides to get:
x+4 = 4(x-1) -4sqrt(x-1) +1
x+4 = 4x-3 - 4sqrt(x-1)
4sqrt(x-1) = 3x-7
Square both sides to get:
16(x-1) = 9x^2-42x+49
9x^2-58x+65=0
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x=[58+-sqrt(58^2-4*9*65)]/18
x = [58 +- sqrt(1024)]/18
x = [58 +- 32]/18
x = [58+32]/18 or x=[58-32]/18
x = 5 or x = 2
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Checking the answers in sqrt(x+4) - 2sqrt(x-1) = -1:
If x=5 you get sqrt(9) -2sqrt4) = -1-----that checks
If x=2 you get sqrt(6) -2sqrt1 = -1------that does not check
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The only solution is x=5
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Cheers,
Stan H.
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