Solve algebraically for the exact values of x:
5X/2 = 1/x + x/4
Answer: ======> x = 2/3, or -2/3 ====> x = 0.666667 or x = −0.666667
Lets Solve Equation:
5x/2 = 1/x + x/4
Multiply all terms by X and Cancel:
5xx / 2 = 1 + xx / 4
5/2x^2 = 1/4x^2 + 1 Simplify Both sides of equation:
5/2x^2 - 1/4x^2 = 1/4x^2 + 1 - 1/4x^2
Subtract 1/4x^2 from both sides:
9/4x^2 = 1
9/4x^2 / 9 / 4 = 1/9 / 4 Divide both sides by 9/4:
x^2 = 4/9
x = +- sqrt 4/9 (Take Square Root):
Answer x = 0.666667, or x = -0.666667
Check Answers:
plug them in to make sure they work:
x = 0.666667 (works in original equation):
x = -0.666667 (works in original equation):
Therefore, the answers, x = 0.666667 or x = -0.666667 =======> x = 2/3, or -2/3
Hope that helps!!!!!!!!!! : )
