Question 1210429
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For the first problem....<br>
NOTE: Don't use "√" when posting problems involving square roots -- or, if you do, enclose the expressions under the radicals in parentheses.  "2(√4x+5)" looks like {{{2sqrt(4x)+5}}}, when apparently the intended expression is 2(√(4x+5)) = {{{2sqrt(4x+5)}}}<br>
Outline for a formal solution....
(1) rewrite the equation with one radical on each side
(2) square both sides of that equation; you will still have a radical on one side
(3) isolate that radical on one side and again square both sides of the equation, resulting finally in an equation without any radicals<br>
If you do all that algebra correctly, you will end up with this quadratic equation: {{{169x^2-874x+145=0}}}<br>
Options for what to do from here....<br>
(1) solve that equation by factoring (have fun!!!)
(2) solve the equation using the quadratic formula (perhaps even MORE fun!!!!)
(3) solve the equation using a graphing calculator (e.g., TI84 or equivalent; or online at desmos.com)
Option (3) is much less work than either of the other options....<br>
But if you are going to solve the problem using technology, why bother with the algebra outlined above?  Simply use a graphing utility to graph the expressions on each side of the original equation and find the x value where the graphs intersect.<br>
Finally, what is the easiest (and by far the fastest) way to solve the problem?<br>
Assume the answer is a whole number; ignore ALL of the above and look for whole number values of x for which (4x+5) and (3x+1) are both perfect squares.<br>
ANSWER: x = 5<br>
CHECK: 2*sqrt(4x+5)-sqrt(3x+1) = 2*sqrt(25)-sqrt(16) = 2(5)-4 = 10-4 = 6<br>