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Maths-

General

Easy

Question

Solve $open parentheses x squared plus 4 x plus 5 close parentheses to the power of 3 over 2 end exponent plus 1 equals 0$

hint Hint:

Rearrange the equation and then solve.

The correct answer is: x = - 2

Complete step by step solution:
Here we have the equation $open parentheses x squared plus 4 x plus 5 close parentheses to the power of 3 over 2 end exponent plus 1 equals 0$
On subtracting 1 from both the sides, we get $open parentheses x squared plus 4 x plus 5 close parentheses to the power of 3 over 2 end exponent equals negative 1$
To make the power of the equation as 1, we have to raise the equation by $2 over 3$
$not stretchy rightwards double arrow open parentheses x squared plus 4 x plus 5 close parentheses to the power of 3 over 2 cross times 2 over 3 end exponent equals negative 1 to the power of 2 over 3 end exponent$
$not stretchy rightwards double arrow open parentheses x squared plus 4 x plus 5 close parentheses to the power of negative 1 end exponent equals cube root of left parenthesis negative 1 right parenthesis squared end root$
$not stretchy rightwards double arrow x squared plus 4 x plus 5 equals cube root of 1$
$not stretchy rightwards double arrow x squared plus 4 x plus 5 equals 1$
On rearranging, we get $x squared plus 4 x plus 4 equals 0$
Now, this is a quadratic equation with a = 1, b = 4, c = 4
Roots can be found with, $x equals fraction numerator negative b plus-or-minus square root of b squared minus 4 a c end root over denominator 2 a end fraction$
$x equals fraction numerator negative 4 plus-or-minus square root of 16 minus 4 cross times 1 cross times 4 end root over denominator 2 cross times 1 end fraction$
On solving, we get x = - 2

Related Questions to study

The suspension cables from the Golden gate bridge’s towers are farther above the roadway near the towers and closer to the roadway near the middle of the bridge. You can figure out your distance from middle of the bridge, x, in feet, and height of the suspension cable, y, in feet, at your position by using the equation x = $fraction numerator square root of y to the power of negative 220 end exponent end root over denominator 0.010583 end fraction$ About how far is the cable from roadway when you are 200 ft from middle of the bridge

The suspension cables from the Golden gate bridge’s towers are farther above the roadway near the towers and closer to the roadway near the middle of the bridge. You can figure out your distance from middle of the bridge, x, in feet, and height of the suspension cable, y, in feet, at your position by using the equation x = $fraction numerator square root of y to the power of negative 220 end exponent end root over denominator 0.010583 end fraction$ About how far is the cable from roadway when you are 200 ft from middle of the bridge