Can you help me solve these problems!!??
1) a^4-10a^2+9
2)2x^2+7x+6
Thank you!! :)
1) a^4-10a^2+9
2)2x^2+7x+6
Thank you!! :)
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1) a^4-10a^2+9
let u = a^2
=> u^2-10u + 9
=> u^2 -u -9u +9
=> u(u -1) -9(u -1)
=> (u -1)(u -9)
=> (a^2 - 1) (a^2 - 9)
2) 2x^2+7x+6
2*6 = 12, 3*4=12 3+4=12
=> 2x^2 +4x +3x +6
=> 2x(x + 2) +3(x +2)
=> (x + 2)(2x + 3)
to find the actual values of a and x you need to what your functions are equal to
let u = a^2
=> u^2-10u + 9
=> u^2 -u -9u +9
=> u(u -1) -9(u -1)
=> (u -1)(u -9)
=> (a^2 - 1) (a^2 - 9)
2) 2x^2+7x+6
2*6 = 12, 3*4=12 3+4=12
=> 2x^2 +4x +3x +6
=> 2x(x + 2) +3(x +2)
=> (x + 2)(2x + 3)
to find the actual values of a and x you need to what your functions are equal to
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1) a^4-10a^2+9 = 0
a^2(a^2 - 10 + 9) = 0
a^2 = 0
a = 0
2. a^2 - 10 + 9 = 0
a^2 - 1 = 0
a^2 = 1
a = +/- 1
2)2x^2+7x+6
(2x + 3)(x + 2)
a^2(a^2 - 10 + 9) = 0
a^2 = 0
a = 0
2. a^2 - 10 + 9 = 0
a^2 - 1 = 0
a^2 = 1
a = +/- 1
2)2x^2+7x+6
(2x + 3)(x + 2)
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We need to know what they're equal to-I'm assuming 0?
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1)
let a^2=x <
therefore x^2-10x+9=0
this is much easier to simplify
put it into two brackets: (x-9)(x-1)=0
therefore x=9 OR x=1
but don't forget we replaced a^2 with x at the beginning.
therefore a^2=9 so a=3
and a^2=1 so a=1
therefore the answers are a=3 OR a=1
2)
With this kind of question, I multiply the two outer numbers so 2x6=12
Then you need to find two numbers which times to make 12, and add to make 7, in this case is 3 and 4. You then factorize this:
2x^2+4x+3x+6=0
2x(x+2)+3(x+2)=0
(2x+3)(x+2)=0
x=-3/2 OR x=-2
I'm so sorry if this doesn't make sense, I'm not very good at explaining but you should get the gist of what I was trying to do (and this is all assuming your equations are equal to 0 - if not, you may have a bit more working out to do)
let a^2=x <
this is much easier to simplify
put it into two brackets: (x-9)(x-1)=0
therefore x=9 OR x=1
but don't forget we replaced a^2 with x at the beginning.
therefore a^2=9 so a=3
and a^2=1 so a=1
therefore the answers are a=3 OR a=1
2)
With this kind of question, I multiply the two outer numbers so 2x6=12
Then you need to find two numbers which times to make 12, and add to make 7, in this case is 3 and 4. You then factorize this:
2x^2+4x+3x+6=0
2x(x+2)+3(x+2)=0
(2x+3)(x+2)=0
x=-3/2 OR x=-2
I'm so sorry if this doesn't make sense, I'm not very good at explaining but you should get the gist of what I was trying to do (and this is all assuming your equations are equal to 0 - if not, you may have a bit more working out to do)