What is the opposite of: (- 3 ) x ( - 2 ) x ( - 6 )
Answers
Step-by-step explanation:
Follow these steps to solve an absolute value equality which contains two absolute values (one on each side of the equation):
Write two equations without absolute values. The first equation will set the quantity inside the bars on the left side equal to the quantity inside the bars on the right side. The second equation will set the quantity inside the bars on the left side equal to the opposite of the quantity inside the bars on the right side.
Solve the two equations
8x
4
−2x
3
−27x
2
+6x+9=0
Let the roots be a,−a, b, c
S
1
=a −a +b +c=−
8
−2
=
4
1
b +c=
4
1
( i )
S
3
=−a
2
b −a b c+ a bc−a
2
c=−
8
6
⇒a
2
(b +c)=
4
3
(ii)
dividing (i) by (ii)
⇒b + c=
4
1
(iii)
S
4
=−a
2
bc=
8
9
⇒bc=−
8
3
(iv)
substituting b from (iii) in (i)
b(
4
1
−b)=−
8
3
4
b−4b
2
=−
8
3
2b−8b
2
=3
8b
2
−2b−3=0
8b
2
+4b−6b−3=0
4b(2b+1)−3(2b+1)=0
(4b−3)(2b+1)=0
⇒b=
4
3
,−
2
1
substituing b in (iv)
⇒c=−
2
1
,
4
3
S
2
=a(−a)+(−a)(b)+bc+ca=
8
−27
⇒−a
2
−ab+bc+ac=
8
−27
The value of 54 is not satisfied for b=−2 1
So the roots of the equation are
3 ,− 3 , 4 3 ,− 2 1