SOLUTION: Please help me solve this problem. 1. Type an exact answer, using radicals as needed. Rationalize all denominators. use a comma to seperate answeres as needed. 15x^4-8x^2+1

Question 268967: Please help me solve this problem.
1. Type an exact answer, using radicals as needed. Rationalize all denominators. use a comma to seperate answeres as needed.
15x^4-8x^2+1=0
Found 3 solutions by stanbon, Alan3354, psbhowmick:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
Type an exact answer, using radicals as needed. Rationalize all denominators. use a comma to seperate answeres as needed.
15x^4-8x^2+1=0
---
Think of two numbers whose product is 1*15 = 15
and whose sum is -8.
The numbers are -5 and -3
---
Change the middle term of your problem to -5x-3x
15x^2-5x-3x+1 = 0
Factor the 1st 2 and the last two terms separately:
5x(3x-1)-(3x-1) = 0
Factor again:
(3x-1)(5x-1) = 0
Solve for "x":
x = 1/3 or x = 1/5
==========================
cheers,
Stan H.
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
15x^4-8x^2+1=0
-------------
It's a quadratic in x^2
Use the quadratic eqn:
x^2 = 1/5, 1/3
------------------
x = +/- sqrt(5)/5
x = +/- sqrt(3)/3

Answer by psbhowmick(878)   (Show Source): You can put this solution on YOUR website!
The equation is .

Substitute .
Thus the equation becomes

Solved by pluggable solver: EXPLAIN simplification of an expression

Your Result:

YOUR ANSWER

This is an equation! Solutions: z=0.333333333333333,z=0.2.

Graphical form: Equation was fully solved.
Text form: 15*z^2-8*z+1=0 simplifies to 0=0
Cartoon (animation) form:
For tutors: simplify_cartoon( 15*z^2-8*z+1=0 )

If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at .
Equation is a quadratic equation: 15*z^2-8*z+1 =0, and has solutions 0.333333333333333,0.2
It becomes .
Result:
This is an equation! Solutions: z=0.333333333333333,z=0.2.

Universal Simplifier and Solver

Done!

Thus z = , .
Hence, x = , i.e. ,
RELATED QUESTIONS
Solve. {{{4x^4-16x^2+15=0}}} The solution is x=____. (Simplify your answer. Type an... (answered by robertb)
Solve: {{{5x^2=15}}} What are the solutions? x=___ (Type an exact answer, using... (answered by stanbon)
Solve 4x^2=20 Find the x-intercepts of f(x)=4x^2-20. What are the solutions? x=?(type... (answered by Fombitz)
Solve. 9x^4-18x^2+5=0 Simplify your answer. Type an exact answer,using radicals as... (answered by stanbon)
Please help me solve {{{x^2+7x-11=0}}} The hint tells me to type a simplified fraction.... (answered by stanbon)
Give exact and approximate solutions to three decimal places. (x-4)^2=24 x= (type an... (answered by solver91311)
6x^4-13x^2+6=0 It asks me to: (Simplify. Type an exact answer using radicals if... (answered by Fombitz)
Type an exact answer, using radicals as needed. Rationalize all denominators. Express... (answered by Alan3354)
I've tried everything but the examples i get don't show me in detail step by step how... (answered by josgarithmetic)