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?
Lv 7
? asked in Science & MathematicsMathematics · 1 month ago

About algebra?

 Prove that sqr[(r(r^2-3))^2-4]/(r^2-1)=sqr(r^2-4), thank in advance.

2 Answers

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  • ?
    Lv 7
    1 month ago

    sqr[(r(r^2-3))^2-4]/(r^2-1)

    =

    sqr[(r^4-6r^2+9)r^2-4]/(r^2-1)

    =

    sqr[r^6-6r^4+9r^2-4]/(r^2-1)

    =

    sqr[(r^2-1)(r^4-5r^2+4)]/(r^2-1)

    =

    sqr[(r^2-1)(r^2-4)(r^2-1)]/(r^2-1)

    =

    sqr[(r^2-4)(r^2-1)^2]/(r^2-1)

    =

    (r^2-1)sqr(r^2-4)/r^2-1)

    =

    sqr(r^2-4)

    This proves that my previous result in another problem

    x+y+z=

    (3/2){r+/-sqr[(r(r^2-3))^2-4]/(r^2-1)} is exactly=

    (3/2)[r+/-sqr(r^2-4)]

    That is what I actually want.

    Stars are awarded to those who

    successfully solves the problem.

  • rotchm
    Lv 7
    1 month ago

    What is strange is that you're a level 7 here and you even solve much much harder problems like differential equations and calculus. Yet you're asking to solve a very easy algebra question?

    Anw, hint: Square both sides. ]

    So, is it true?

    Or, can you find a counterexample?

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