SOLUTION: Solve for x: {{{sqrt (7x) -sqrt (3x) =4}}}

Algebra ->  Square-cubic-other-roots -> SOLUTION: Solve for x: {{{sqrt (7x) -sqrt (3x) =4}}}      Log On


   

Question 1113650: Solve for x:
sqrt+%287x%29+-sqrt+%283x%29+=4
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39625) About Me  (Show Source):
Answer by ikleyn(52855) About Me  (Show Source):
You can put this solution on YOUR website!
.
sqrt+%287x%29 -sqrt+%283x%29 = 4


%28sqrt%287%29+-+sqrt%283%29%29.sqrt%28x%29 = 4


sqrt%28x%29 = 4%2F%28sqrt%287%29-sqrt%283%29%29 = rationalize the fraction = 4%2F%28sqrt%287%29-sqrt%283%29%29.%28sqrt%287%29%2Bsqrt%283%29%29%2F%28sqrt%287%29%2Bsqrt%283%29%29 =  = %284%2A%28sqrt%287%29%2Bsqrt%283%29%29%29%2F%287-3%29 = sqrt%287%29%2Bsqrt%283%29  ====>


x = %28sqrt%287%29+%2B+sqrt%283%29%29%5E2 = 7+%2B+3+%2B+2%2Asqrt%287%2A3%29 = 10%2B2%2Asqrt%2821%29 = 19.165 (approximately).