Maths-
General
Easy

Question

What are the solutions to the equation left parenthesis x plus 18 right parenthesis to the power of 3 over 2 end exponent equals left parenthesis x minus 2 right parenthesis cubed

Hint:

Rearrange the equation and then solve for x.

The correct answer is: ⇒ x = 7, -2


    Complete step by step solution:
    Here we have the equation open parentheses x to the power of blank plus 18 close parentheses to the power of 3 over 2 end exponent equals left parenthesis x minus 2 right parenthesis cubed
    To make the power of the equation as 1, we have to raise the equation by 2 over 3
    not stretchy rightwards double arrow left parenthesis x plus 18 right parenthesis to the power of 3 over 2 cross times 2 over 3 end exponent equals left parenthesis x minus 2 right parenthesis to the power of 3 cross times 2 over 3 end exponent
    not stretchy rightwards double arrow x plus 18 equals left parenthesis x minus 2 right parenthesis squared
    table attributes columnalign right columnspacing 0em end attributes row cell not stretchy rightwards double arrow x plus 18 equals x squared minus 4 x plus 4 end cell end table
    On rearranging, we get x squared minus 4 x plus 4 minus x minus 18 equals 0
    not stretchy rightwards double arrow x squared minus 5 x minus 14 equals 0
    Now, this is a quadratic equation with a = 1, b = -5, c = -14
    Roots can be found with, x equals fraction numerator negative b plus-or-minus square root of b squared minus 4 a c end root over denominator 2 a end fraction
    x equals fraction numerator 5 plus-or-minus square root of 25 minus 4 cross times 1 cross times negative 14 end root over denominator 2 cross times 1 end fraction
    x equals fraction numerator 5 plus-or-minus square root of 81 over denominator 2 end fraction
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell not stretchy rightwards double arrow x equals fraction numerator 5 plus-or-minus 9 over denominator 2 end fraction end cell row cell not stretchy rightwards double arrow x equals 7 comma negative 2 end cell end table

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