SOLUTION: root{x+1} + root of (2x-3} =4.find x

Algebra ->  Radicals -> SOLUTION: root{x+1} + root of (2x-3} =4.find x      Log On


   

Question 1151032: root{x+1} + root of (2x-3} =4.find x
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%28x%2B1%29%2B+sqrt%282x-3%29+=4....find x
sqrt%28x%2B1%29=4-+sqrt%282x-3%29+.......square both sides

x%2B1=16-+8sqrt%282x-3%29%2B2x-3.......move 8sqrt%282x-3%29 to the left and x%2B1 to the right
8sqrt%282x-3%29=16-+x-1%2B2x-3
8sqrt%282x-3%29=12%2Bx......square both sides again
8%5E2%28sqrt%282x-3%29%29%5E2=%2812%2Bx%29%5E2
64%282x-3%29=12%5E2%2B24x%2Bx%5E2

0=x%5E2-104x%2B336...switch sides

x%5E2-104x%2B336=0.........use quadratic formula

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-%28-104%29+%2B-+sqrt%28+%28-104%29%5E2-4%2A1%2A336+%29%29%2F%282%2A1%29+

x+=+%28104+%2B-+sqrt%2810816-1344%29%29%2F2+

x+=+%28104+%2B-+sqrt%289472%29%29%2F2+
x+=+%28104+%2B-+sqrt%28+37%2A256+%29%29%2F2+
x+=+%28104+%2B-+16sqrt%28+37+%29%29%2F2+
x+=+%28cross%28104%2952+%2B-+cross%2816%298sqrt%28+37+%29%29%2Fcross%282%291+

x+=+%2852+%2B-+8sqrt%28+37+%29%29+
solutions:

x+=+52+%2B+8sqrt%28+37+%29+
x+=+52+-+8sqrt%28+37+%29+