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2 years ago

Can somebody help me pls

Mathematics

1 answer:

SSSSS [86.1K]2 years ago

5 0

the answer can vary between x=−1 or x=2 or x=−3 or x=3

explanation:

x4−x3−11x2+9x+18=0

Step 1: Factor left side of equation.

(x+1)(x−2)(x+3)(x−3)=0

Step 2: Set factors equal to 0.

x+1=0 or x−2=0 or x+3=0 or x−3=0

x=−1 or x=2 or x=−3 or x=3

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2 years ago

Solve for x:a(a²+b²)x²+b²x-a

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Answer:

x = a/(a² + b²) or x = -1/a

Step-by-step explanation:

a(a²+ b²)x² + b²x - a =0

Use the quadratic equation formula:

$x = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a} =\dfrac{-b\pm\sqrt{D}}{2a}$

1. Evaluate the discriminant D

D = b² - 4ac = b⁴ - 4a(a² + b²)(-a) = b⁴ + 4a⁴ + 4a²b² = (b² + 2a²)²

2. Solve for x

$\begin{array}{rcl}x & = & \dfrac{-b\pm\sqrt{D}}{2a}\\\\ & = & \dfrac{-b^{2}\pm\sqrt{(b^{2}+2a^{2})^{2}}}{2a(a^{2} + b^{2})}\\\\ & = & \dfrac{-b^{2}\pm(b^{2}+ 2a^{2})}{2a(a^{2} + b^{2})}\\\\x = \dfrac{-b^{2}+(b^{2} + 2a^{2})}{2a(a^{2} + b^{2})}&\qquad& x =\dfrac{-b^{2}-(b^{2} + 2a^{2})}{2a(a^{2} + b^{2})}\\\\x =\dfrac{-b^{2}+(b^{2} + 2a^{2})}{2a(a^{2} + b^{2})}&\qquad& x =\dfrac{-b^{2}-(b^{2} +2a^{2})}{2a(a^{2} + b^{2})}\\\\\end{array}$

$\begin{array}{rcl}x = \large \boxed{\mathbf{\dfrac{a}{a^{2} + b^{2}}}}&\qquad& x =\dfrac{-b^{2}-(b^{2} +2a^{2})}{2a(a^{2} + b^{2})}\\\\&\qquad& x =\dfrac{-2b^{2}- 2a^{2}}{2a(a^{2} + b^{2})}\\\\&\qquad& x =\dfrac{-2(a^{2}+ b^{2})}{2a(a^{2} + b^{2})}\\\\&\qquad& x =\large \boxed{\mathbf{-\dfrac{1}{a}}}\\\\\end{array}$

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3 years ago

Given triangle DEF where ∠D = (7b +1)∘, ∠E = (2b + 1)∘, and ∠F = ( b + 8)∘. What is the measure of ∠E?

____ [38]

<h3>Answer: 35 (choice C)</h3>

=============================================

Explanation:

For any triangle, the three interior angles always add to 180.

D+E+F = 180

(7b+1) + (2b+1) + (b+8) = 180

(7b+2b+b) + (1+1+8) = 180

10b+10 = 180

10b = 180-10

10b = 170

b = 170/10

b = 17

Use this value of b to find the three angle measures

D = 7b+1 = 7*17+1 = 119+1 = 120
E = 2b+1 = 2*17+1 = 34+1 = 35 degrees
F = b+8 = 17+8 = 25

As a check,

D+E+F = 120+35+25 = 120+60 = 180

which helps confirm the correct answers.

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