(x+3)^2 + 16/(x+3)^2 = 92 x + 1/(x+3) = ??
1 answer:
One
Remark
This is very complicate unless you pick the right method. It's very handy o know about substitutions.
Method
Let z = (k + 2)^2
Now the problem becomes
z + 16/z = 92 Multiply through by z
Solution
z^2 + 16 = 92z
That does not look very promising. If you know the quadratic formula, this mess can be solved. If you do not know what the quadratic formula is, then what I've written is the answer.
Worse yet, you have to know what complex numbers are. Is this something you know about? The z form of this equation is fine. It gives answers that are rational. The problem is that both are negative and so in your next step, you will be forced to take the square root of a negative number.
Maybe the answer is just
(x + 3)^ + 16 = 92(x + 3)^2
If all you have to do is expand this then you get
x^2 + 6x + 9 + 16 = 92(x^2 + 6x + 9) Remove the brackets.
x^2 + 6x + 25 = 92x^2 + 552x + 828 Put the left over to the right.
0 = 92x^2 - x^2 + 552x - 6x + 828 - 25
0 = 91x^1 + 546x + 803
It looks that way from the second question. If I'm wrong about that, put a comment down below.
Two
Put over a common denominator and expand
Remark
This is very complicate unless you pick the right method. It's very handy o know about substitutions.
Method
Let z = (k + 2)^2
Now the problem becomes
z + 16/z = 92 Multiply through by z
Solution
z^2 + 16 = 92z
That does not look very promising. If you know the quadratic formula, this mess can be solved. If you do not know what the quadratic formula is, then what I've written is the answer.
Worse yet, you have to know what complex numbers are. Is this something you know about? The z form of this equation is fine. It gives answers that are rational. The problem is that both are negative and so in your next step, you will be forced to take the square root of a negative number.
Maybe the answer is just
(x + 3)^ + 16 = 92(x + 3)^2
If all you have to do is expand this then you get
x^2 + 6x + 9 + 16 = 92(x^2 + 6x + 9) Remove the brackets.
x^2 + 6x + 25 = 92x^2 + 552x + 828 Put the left over to the right.
0 = 92x^2 - x^2 + 552x - 6x + 828 - 25
0 = 91x^1 + 546x + 803
It looks that way from the second question. If I'm wrong about that, put a comment down below.
Two
Put over a common denominator and expand
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<span><u><em>The correct answers are: </em></u>
1) f(x)=1/2x;
2) f(x)=2x+1;
3) f(x)=x^3;
4) f(x)=6x.
<u><em>Explanation</em></u><span><u><em>: </em></u>
Let x be the input. In function notation, the output is denoted by f(x).
For #1, since the output is half of the input, we want to take half of x; this would give us
f (x)=</span></span>
<span><span>x.
For #2, twice the input is 2x; one more than this is 2x+1, which gives us
f (x)=2x+1.
For #3, the cube of the input is x</span></span>³<span><span>, which gives us
f (x)=x</span></span>³<span><span>.
For #4, six times the input is 6x, which gives us
f (x)=6x.</span></span>
1) f(x)=1/2x;
2) f(x)=2x+1;
3) f(x)=x^3;
4) f(x)=6x.
<u><em>Explanation</em></u><span><u><em>: </em></u>
Let x be the input. In function notation, the output is denoted by f(x).
For #1, since the output is half of the input, we want to take half of x; this would give us
f (x)=</span></span>
For #2, twice the input is 2x; one more than this is 2x+1, which gives us
f (x)=2x+1.
For #3, the cube of the input is x</span></span>³<span><span>, which gives us
f (x)=x</span></span>³<span><span>.
For #4, six times the input is 6x, which gives us
f (x)=6x.</span></span>