Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation 2*cos(x)+1=0
-
Equation sqrt(x+1)=1-x
- Equation x^4-7x^2-18=0
-
Equation (x+10)(-x-8)=0
- Express {x} in terms of y where:
- 16*x-17*y=-9
- 7*x-2*y=20
- -12*x-3*y=-9
- 20*x+4*y=-7
- Integral of d{x}:
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sqrt(x+1)
- Derivative of:
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sqrt(x+1)
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1-x
- Graphing y =:
- sqrt(x+1)
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1-x
- Limit of the function:
-
1-x
-
Identical expressions
- sqrt(x+ one)= one -x
- square root of (x plus 1) equally 1 minus x
- square root of (x plus one) equally one minus x
- √(x+1)=1-x
- sqrtx+1=1-x
-
Similar expressions
- f*x=-2*sqrt(x)+12*x^4-3*sin(x)+9*acos(x)-5
- x-7sqrt(x)+10=0
- 27(1/3x-1)(1/9x^2+1/3x+1)-x(x-1)(x+1)=2x^2
- sqrt(x+1)=1+x
- sqrt(x-1)=1-x
- 2^sqrt(x)+1-2^(sqrt(x)+1)-2^(sqrt(x)-1)=12
sqrt(x+1)=1-x equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\sqrt{x + 1} = 1 - x$$
$$\sqrt{x + 1} = 1 - x$$
We raise the equation sides to 2-th degree
$$x + 1 = \left(1 - x\right)^{2}$$
$$x + 1 = x^{2} - 2 x + 1$$
Transfer the right side of the equation left part with negative sign
$$- x^{2} + 3 x = 0$$
This equation is of the form
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = -1$$
$$b = 3$$
$$c = 0$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 0$$
$$x_{2} = 3$$
Because
$$\sqrt{x + 1} = 1 - x$$
and
$$\sqrt{x + 1} \geq 0$$
then
$$1 - x \geq 0$$
or
$$x \leq 1$$
$$-\infty < x$$
The final answer:
$$x_{1} = 0$$
$$\sqrt{x + 1} = 1 - x$$
$$\sqrt{x + 1} = 1 - x$$
We raise the equation sides to 2-th degree
$$x + 1 = \left(1 - x\right)^{2}$$
$$x + 1 = x^{2} - 2 x + 1$$
Transfer the right side of the equation left part with negative sign
$$- x^{2} + 3 x = 0$$
This equation is of the form
a*x^2 + b*x + c = 0
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = -1$$
$$b = 3$$
$$c = 0$$
, then
D = b^2 - 4 * a * c =
(3)^2 - 4 * (-1) * (0) = 9
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 0$$
$$x_{2} = 3$$
Because
$$\sqrt{x + 1} = 1 - x$$
and
$$\sqrt{x + 1} \geq 0$$
then
$$1 - x \geq 0$$
or
$$x \leq 1$$
$$-\infty < x$$
The final answer:
$$x_{1} = 0$$
The graph