Solving functions.

Question

0

716

1

How do you solve these? For some reason the answers I get with these look so wrong to me.

Guest Jun 7, 2019

+9488

+4

Best Answer

a.__	-4x⁶ = -2916	___	Divide both sides of the equation by -4
	x⁶ = 729		Take the ± 6th root of both sides
	x = $\pm\sqrt[6]{729}$		Plug this into a calculator or note that 3⁶ = 729 so we can rewrite 729 as 3⁶
	x = $\pm\sqrt[6]{3^6}$		Simplify
	x = ± 3
	This equation has two solutions. There are two values of x which make the equation true. They are: x = 3 and x = -3

b.	93 - 7x³ = 23		Subtract 93 from both sides of the equation.
	-7x³ = -70		Divide both sides of the equation by -7
	x³ = 10		Take the cube root of both sides.
	x = $\sqrt[3]{10}$		To get an approximate solution, plug $\sqrt[3]{10}$ into a calculator.
	x ≈ 2.154

c.	(-5p)⁵ = -65		Take the fifth root of both sides.
	-5p = $\sqrt[5]{-65}$		Divide both sides by -5
	p = $\frac{\sqrt[5]{-65}}{-5}$		SImplify
	p = $\frac{\sqrt[5]{-1}\,\cdot\,\sqrt[5]{65}}{-5}$
	p = $\frac{-1\ \cdot\ \sqrt[5]{65}}{-5}$
	p = $\frac{\sqrt[5]{65}}{5}$
	p ≈ 0.461

d.	$-7+\frac{14}{x-3}\ =\ -5$		Add 7 to both sides.
	$\frac{14}{x-3}\ =\ 2$		Multiply both sides by (x - 3) and note x ≠ 3
	14 = 2(x - 3)		Divide both sides by 2
	7 = x - 3		Add 3 to both sides
	10 = x
	x = 10

hectictar Jun 7, 2019

hectictar · Answer 1 · 2019-06-07T09:33:42

a.__	-4x⁶ = -2916	___	Divide both sides of the equation by -4
	x⁶ = 729		Take the ± 6th root of both sides
	x = $\pm\sqrt[6]{729}$		Plug this into a calculator or note that 3⁶ = 729 so we can rewrite 729 as 3⁶
	x = $\pm\sqrt[6]{3^6}$		Simplify
	x = ± 3
	This equation has two solutions. There are two values of x which make the equation true. They are: x = 3 and x = -3

b.	93 - 7x³ = 23		Subtract 93 from both sides of the equation.
	-7x³ = -70		Divide both sides of the equation by -7
	x³ = 10		Take the cube root of both sides.
	x = $\sqrt[3]{10}$		To get an approximate solution, plug $\sqrt[3]{10}$ into a calculator.
	x ≈ 2.154

c.	(-5p)⁵ = -65		Take the fifth root of both sides.
	-5p = $\sqrt[5]{-65}$		Divide both sides by -5
	p = $\frac{\sqrt[5]{-65}}{-5}$		SImplify
	p = $\frac{\sqrt[5]{-1}\,\cdot\,\sqrt[5]{65}}{-5}$
	p = $\frac{-1\ \cdot\ \sqrt[5]{65}}{-5}$
	p = $\frac{\sqrt[5]{65}}{5}$
	p ≈ 0.461

d.	$-7+\frac{14}{x-3}\ =\ -5$		Add 7 to both sides.
	$\frac{14}{x-3}\ =\ 2$		Multiply both sides by (x - 3) and note x ≠ 3
	14 = 2(x - 3)		Divide both sides by 2
	7 = x - 3		Add 3 to both sides
	10 = x
	x = 10