Answer
Step-by-step explanation:
b)x=-1,-3
X + 3 = 9-4
First simplify the right side.
9-4 = 5
Now you have x + 3 = 5
Now subtract 3 from both sides:
X = 2
Answer: x = 2
Answer:
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Answer:
The cubic function is f(x) = (27/32)·x - 3/32·x³ - -9/32·x² - 9/32
Step-by-step explanation:
The given function is f(x) = a·x³ + b·x² + c·x + d
By differentiation, we have;
3·a·x² + 2·b·x + c = 0
3·a·(-3)² + 2·b·(-3) + c = 0
3·a·9 - 6·b + c = 0
27·a - 6·b + c = 0
3·a·(1)² + 2·b·(1) + c = 0
3·a + 2·b + c = 0
a·(-3)³ + b·(-3)² + c·(-3) + d = -3
-27·a + 9·b - 3·c + d = -3...(1)
a + b + c + d = 0...(2)
Subtracting equation (1) from equation (2) gives;
28·a - 8·b + 4·c = 3
Therefore, we have;
27·a - 6·b + c = 0
3·a + 2·b + c = 0
28·a - 8·b + 4·c = 0
Solving the system of equations using an Wolfram Alpha gives;
a = -3/32, b = -9/32, c = 27/32 from which we have;
a + b + c + d = 0 3 × (-3/32) + 2 × (-9/32) + (27/32) + d = 0
d = 0 - (0 3 × (-3/32) + 2 × (-9/32) + (27/32)) = -9/32
The cubic function is therefore f(x) = (-3/32)·x³ + (-9/32)·x² + (27/32)·x + (-9/32).
Answer: (6a + 5b) • (6a - 5b)
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "b2" was replaced by "b^2". 1 more similar replacement(s).
Step by step solution :
Step 1 :
Equation at the end of step 1 :
(36 • (a2)) - 52b2
Step 2 :
Equation at the end of step 2 :
(22•32a2) - 52b2
Step 3 :
Trying to factor as a Difference of Squares :
3.1 Factoring: 36a2-25b2
Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : 36 is the square of 6
Check : 25 is the square of 5
Check : a2 is the square of a1
Check : b2 is the square of b1
Factorization is : (6a + 5b) • (6a - 5b)
Final result :
(6a + 5b) • (6a - 5b)
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