Answer:
0
Step-by-step explanation:
17.
(x - 1/x ) = 7
Square both sides
x^2 + 1/x^2 - 2 = 49
x^2 + 1/x^2 = 51.
18.
To find the values of "a" and "b," we can use the fact that "x + 1" and "x - 1" are factors of the given polynomial.
When a polynomial is divided by a factor, the remainder is always zero. Therefore, we can set up the following equations:
For "x + 1" as a factor:
Substitute "-1" for "x" in the polynomial: a(-1)^3 + (-1)^2 - 2(-1) + b = 0.
Simplify the equation: -a + 1 + 2 + b = 0.
Combine like terms: -a + b + 3 = 0.
For "x - 1" as a factor:
Substitute "1" for "x" in the polynomial: a(1)^3 + (1)^2 - 2(1) + b = 0.
Simplify the equation: a + 1 - 2 + b = 0.
Combine like terms: a + b - 1 = 0.
Now we have a system of two equations with two variables:
-a + b + 3 = 0
a + b - 1 = 0
We can solve this system of equations simultaneously.
Adding both equations together, we get:
(-a + b + 3) + (a + b - 1) = 0 + 0
b + b + 3 - 1 = 0
2b + 2 = 0
Subtracting 2 from both sides, we have:
2b = -2
Dividing by 2, we get:
b = -1
Substituting the value of "b" back into one of the equations, we can find "a":
a + (-1) - 1 = 0
a - 2 = 0
a = 2
Therefore, the values of "a" and "b" are:
Is it ok
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Answers & Comments
Answer:
0
Step-by-step explanation:
Verified answer
Step-by-step explanation:
17.
(x - 1/x ) = 7
Square both sides
x^2 + 1/x^2 - 2 = 49
x^2 + 1/x^2 = 51.
18.
To find the values of "a" and "b," we can use the fact that "x + 1" and "x - 1" are factors of the given polynomial.
When a polynomial is divided by a factor, the remainder is always zero. Therefore, we can set up the following equations:
For "x + 1" as a factor:
Substitute "-1" for "x" in the polynomial: a(-1)^3 + (-1)^2 - 2(-1) + b = 0.
Simplify the equation: -a + 1 + 2 + b = 0.
Combine like terms: -a + b + 3 = 0.
For "x - 1" as a factor:
Substitute "1" for "x" in the polynomial: a(1)^3 + (1)^2 - 2(1) + b = 0.
Simplify the equation: a + 1 - 2 + b = 0.
Combine like terms: a + b - 1 = 0.
Now we have a system of two equations with two variables:
-a + b + 3 = 0
a + b - 1 = 0
We can solve this system of equations simultaneously.
Adding both equations together, we get:
(-a + b + 3) + (a + b - 1) = 0 + 0
b + b + 3 - 1 = 0
2b + 2 = 0
Subtracting 2 from both sides, we have:
2b = -2
Dividing by 2, we get:
b = -1
Substituting the value of "b" back into one of the equations, we can find "a":
a + (-1) - 1 = 0
a - 2 = 0
a = 2
Therefore, the values of "a" and "b" are:
a = 2
b = -1
Is it ok
Thanks