Answer:
119
Step-by-step explanation:
I believe you meant the question to be " [tex]m^4[/tex] + 1 / [tex]m^4[/tex], if m - 1 / m = 3. "
I presume that we want to take this second equation at hand here, and " simplify " it further. After doing so this first expression will have a value with respect to the simplified value of the equation, and, plugging in it's value we can solve for the expression ( [tex]m^4[/tex] + 1 / [tex]m^4[/tex]. )
m - 1 / m = 3 - Take each value squared on either side of the equation,
[tex]( m - 1 / m )^2 = 3^2[/tex] - Simplify,
[tex]( m - 1 / m )^2 = 9[/tex]
If you don't know how to expand expressions such as the one in the third step, " [tex]( m - 1 / m )^2[/tex] " here is a quick recap. Remember that [tex]( a - b )^2 = a^2 - 2ab + b^2[/tex]. Therefore,
[tex]( m - 1 / m )^2 = m^2 - 2( m )( 1 / m ) + ( 1 / m )^2,\\( m - 1 / m )^2 = m^2 - 2 + 1 / m^2[/tex]
Now let's continue,
[tex]m^2 - 2 + 1 / m^2 = 9[/tex] - Add 2 on either side,
[tex]m^2 + 1 / m^2 = 11[/tex]
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So now we have the " simplified equation " as you can say, for the equation. Let's " simplify " the expression now,
[tex]m^4+1/m^4 = 75+4(m^2+1/m^2)[/tex] - Substitute the value of 11,
[tex]m^4+1/m^4 = 75+4(11),\\m^4 + 1 / m^4 = 119[/tex]
Solution = 119
