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Maths-

General

Easy

Question

What are the solutions to the equation $open parentheses x squared plus 5 x plus 5 close parentheses to the power of 5 over 2 end exponent equals 1$

hint Hint:

Rearrange the equation and then solve for x.

The correct answer is: ⇒ x = -4, -1

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

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