Mister Exam
Other calculators
-
How to use it?
- Equation:
- Equation ax=b
- Equation x^2+y^2=1
-
Equation x^2-8x+16=0
-
Equation x^4=81
- Express {x} in terms of y where:
- -4*x+7*y=-16
- -1*x-20*y=1
- 14*x-10*y=-4
- -11*x+16*y=3
- Integral of d{x}:
- (y-1)^2
-
Identical expressions
- (y- one)^ two
- (y minus 1) squared
- (y minus one) to the power of two
- (y-1)2
- y-12
- (y-1)²
- (y-1) to the power of 2
- y-1^2
-
Similar expressions
- (y+1)^2
(y-1)^2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Expand the expression in the equation
$$\left(y - 1\right)^{2} = 0$$
We get the quadratic equation
$$y^{2} - 2 y + 1 = 0$$
This equation is of the form
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$y_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$y_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 1$$
$$b = -2$$
$$c = 1$$
, then
Because D = 0, then the equation has one root.
$$y_{1} = 1$$
$$\left(y - 1\right)^{2} = 0$$
We get the quadratic equation
$$y^{2} - 2 y + 1 = 0$$
This equation is of the form
a*y^2 + b*y + c = 0
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$y_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$y_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 1$$
$$b = -2$$
$$c = 1$$
, then
D = b^2 - 4 * a * c =
(-2)^2 - 4 * (1) * (1) = 0
Because D = 0, then the equation has one root.
y = -b/2a = --2/2/(1)
$$y_{1} = 1$$