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- Equation:
- Equation 4b^2=144
-
Equation 29+y*4=309
-
Equation sinx=-1/2
- Equation z^4-2z^2+4=0
- Express {x} in terms of y where:
- sqrt(x^2+y^2+4x-6y-12)+(x^2+10x-27)=8-|y-9|+|y-3|
- -1*x-19*y=-10
- (x^2+y^2-1)^3+x^2*y^3=0
- 4*x-16*y=6
- Derivative of:
- 144
- Sum of series:
-
144
- Canonical form:
- 144
-
Identical expressions
- 4b^ two = one hundred and forty-four
- 4b squared equally 144
- 4b to the power of two equally one hundred and forty minus four
- 4b2=144
- 4b²=144
- 4b to the power of 2=144
4b^2=144 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Move right part of the equation to
left part with negative sign.
The equation is transformed from
$$4 b^{2} = 144$$
to
$$4 b^{2} - 144 = 0$$
This equation is of the form
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$b_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$b_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 4$$
$$b = 0$$
$$c = -144$$
, then
Because D > 0, then the equation has two roots.
or
$$b_{1} = 6$$
$$b_{2} = -6$$
left part with negative sign.
The equation is transformed from
$$4 b^{2} = 144$$
to
$$4 b^{2} - 144 = 0$$
This equation is of the form
a*b^2 + b*b + c = 0
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$b_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$b_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 4$$
$$b = 0$$
$$c = -144$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (4) * (-144) = 2304
Because D > 0, then the equation has two roots.
b1 = (-b + sqrt(D)) / (2*a)
b2 = (-b - sqrt(D)) / (2*a)
or
$$b_{1} = 6$$
$$b_{2} = -6$$
Vieta's Theorem
rewrite the equation
$$4 b^{2} = 144$$
of
$$a b^{2} + b^{2} + c = 0$$
as reduced quadratic equation
$$b^{2} + \frac{b^{2}}{a} + \frac{c}{a} = 0$$
$$b^{2} - 36 = 0$$
$$b^{2} + b p + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = -36$$
Vieta Formulas
$$b_{1} + b_{2} = - p$$
$$b_{1} b_{2} = q$$
$$b_{1} + b_{2} = 0$$
$$b_{1} b_{2} = -36$$
$$4 b^{2} = 144$$
of
$$a b^{2} + b^{2} + c = 0$$
as reduced quadratic equation
$$b^{2} + \frac{b^{2}}{a} + \frac{c}{a} = 0$$
$$b^{2} - 36 = 0$$
$$b^{2} + b p + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = -36$$
Vieta Formulas
$$b_{1} + b_{2} = - p$$
$$b_{1} b_{2} = q$$
$$b_{1} + b_{2} = 0$$
$$b_{1} b_{2} = -36$$
Sum and product of roots
[src]
sum
-6 + 6
$$-6 + 6$$
=
0
$$0$$
product
-6*6
$$- 36$$
=
-36
$$-36$$
-36