SOLUTION: √(x-3)+ √(x+5)= 4 Thanks so much in advance:)

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Question 813745: √(x-3)+ √(x+5)= 4
Thanks so much in advance:)
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
Requires squaring TWICE.

The first squaring:
x-3%2B2%2Asqrt%28x-3%29sqrt%28x%2B5%29%2Bx%2B5=16
2%2Asqrt%28x-3%29sqrt%28x%2B5%29=16%2B3-x
2%2Asqrt%28x-3%29sqrt%28x%2B5%29=19-x

The second squaring:
4%2A%28x-3%29%28x%2B5%29=%2819-x%29%5E2
.
and YOU continue from here. This will be a quadratic equation in x which you can solve by general solution to a quadratic equation, or possibly by factoring.

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!

√(x-3)+ √(x+5)= 4
Thanks so much in advance:)

sqrt%28x+-+3%29+%2B+sqrt%28x+%2B+5%29+=+4

sqrt%28x+-+3%29+=+4+-+sqrt%28x+%2B+5%29 ----- Subtracting sqrt%28x+%2B+5%29 from each side

%28sqrt%28x+-+3%29%29%5E2+=+%284+-+sqrt%28x+%2B+5%29%29%5E2 ------ Squaring both sides of equation

x+-+3+=+16+-+4sqrt%28x+%2B+5%29+-+4sqrt%28x+%2B+5%29+%2B+x+%2B+5

x+-+3+=+16+-+8sqrt%28x+%2B+5%29+%2B+x+%2B+5

x+-+3+=+16+%2B+x+%2B+5+-+8sqrt%28x+%2B+5%29

x+-+3+=+21+%2B+x+-+8sqrt%28x+%2B+5%29

x+-+x+-+3+-+21+=+-+8sqrt%28x+%2B+5%29

-+24+=+-+8sqrt%28x+%2B+5%29

%28-+24%29%5E2+=+%28-+8sqrt%28x+%2B+5%29%29%5E2 ------ Squaring both sides of equation

576+=+64%28x+%2B+5%29

576 = 64x + 320

64x = 576 - 320

64x = 256

x+=+256%2F64, or highlight_green%28x+=+4%29

You can do the check!!

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