Câu hỏi
Factor the expression
(a−2)(a+2)(a2+3)
Evaluate
a4−12−a2
Reorder the terms
a4−a2−12
Rewrite the expression
a4+(3−4)a2−12
Calculate
a4+3a2−4a2−12
Rewrite the expression
a2×a2+a2×3−4a2−4×3
Factor out a2 from the expression
a2(a2+3)−4a2−4×3
Factor out −4 from the expression
a2(a2+3)−4(a2+3)
Factor out a2+3 from the expression
(a2−4)(a2+3)
Giải pháp
(a−2)(a+2)(a2+3)
Hiển thị giải pháp
Find the roots
a1=−3×i,a2=3×i,a3=−2,a4=2
Alternative Form
a1≈−1.732051i,a2≈1.732051i,a3=−2,a4=2
Evaluate
a4−12−a2
To find the roots of the expression,set the expression equal to 0
a4−12−a2=0
Factor the expression
(a−2)(a+2)(a2+3)=0
Separate the equation into 3 possible cases
a−2=0a+2=0a2+3=0
Solve the equation
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Evaluate
a−2=0
Move the constant to the right-hand side and change its sign
a=0+2
Removing 0 doesn't change the value,so remove it from the expression
a=2
a=2a+2=0a2+3=0
Solve the equation
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Evaluate
a+2=0
Move the constant to the right-hand side and change its sign
a=0−2
Removing 0 doesn't change the value,so remove it from the expression
a=−2
a=2a=−2a2+3=0
Solve the equation
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Evaluate
a2+3=0
Move the constant to the right-hand side and change its sign
a2=0−3
Removing 0 doesn't change the value,so remove it from the expression
a2=−3
Take the root of both sides of the equation and remember to use both positive and negative roots
a=±−3
Simplify the expression
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Evaluate
−3
Evaluate the power
3×−1
Evaluate the power
3×i
a=±(3×i)
Separate the equation into 2 possible cases
a=3×ia=−3×i
a=2a=−2a=3×ia=−3×i
Giải pháp
a1=−3×i,a2=3×i,a3=−2,a4=2
Alternative Form
a1≈−1.732051i,a2≈1.732051i,a3=−2,a4=2
Hiển thị giải pháp