Mister Exam
Other calculators
- Square Inequality Step-by-Step
- Inequality with the module Step by Step
- Logarithmic inequality online
-
How to use it?
- Inequation:
-
49-25x<0
- -x-8(2x-1)<3x
- (4x-2x^2-4)/(x^2+2x+1)<=0
- cos3x>=sqrt-2/2
- Graphing y =:
- sqrt(x^2-x-1)
- Derivative of:
-
sqrt(x^2-x-1)
- sqrt(x+7)
- Integral of d{x}:
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sqrt(x+7)
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Identical expressions
- sqrt(x^ two -x- one)>sqrt(x+ seven)
- square root of (x squared minus x minus 1) greater than square root of (x plus 7)
- square root of (x to the power of two minus x minus one) greater than square root of (x plus seven)
- √(x^2-x-1)>√(x+7)
- sqrt(x2-x-1)>sqrt(x+7)
- sqrtx2-x-1>sqrtx+7
- sqrt(x²-x-1)>sqrt(x+7)
- sqrt(x to the power of 2-x-1)>sqrt(x+7)
- sqrtx^2-x-1>sqrtx+7
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Similar expressions
- sqrt(x^2-x+1)>sqrt(x+7)
- sqrt(x^2-x-1)>sqrt(x-7)
- sqrt(x^2+x-1)>sqrt(x+7)
- sqrt(x^2−x−56)−sqrt(x^2−25x+136)<8sqrt((x+7)/(x-8))
- sqrt(x+78)>x+6
- sqrt(x)+6>sqrt(x)+7+sqrt(2*x)-5
sqrt(x^2-x-1)>sqrt(x+7) inequation
The solution
You have entered
[src]
____________ / 2 _______ \/ x - x - 1 > \/ x + 7
$$\sqrt{x^{2} - x - 1} > \sqrt{x + 7}$$
sqrt(x^2 - x - 1*1) > sqrt(x + 7)
Detail solution
Given the inequality:
$$\sqrt{x^{2} - x - 1} > \sqrt{x + 7}$$
To solve this inequality, we must first solve the corresponding equation:
$$\sqrt{x^{2} - x - 1} = \sqrt{x + 7}$$
Solve:
$$x_{1} = -2$$
$$x_{2} = 4$$
$$x_{1} = -2$$
$$x_{2} = 4$$
This roots
$$x_{1} = -2$$
$$x_{2} = 4$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} < x_{1}$$
For example, let's take the point
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$-2 - \frac{1}{10}$$
=
$$- \frac{21}{10}$$
substitute to the expression
$$\sqrt{x^{2} - x - 1} > \sqrt{x + 7}$$
$$\sqrt{\left(-1\right) 1 - - \frac{21}{10} + \left(- \frac{21}{10}\right)^{2}} > \sqrt{- \frac{21}{10} + 7}$$
one of the solutions of our inequality is:
$$x < -2$$
Other solutions will get with the changeover to the next point
etc.
The answer:
$$x < -2$$
$$x > 4$$
$$\sqrt{x^{2} - x - 1} > \sqrt{x + 7}$$
To solve this inequality, we must first solve the corresponding equation:
$$\sqrt{x^{2} - x - 1} = \sqrt{x + 7}$$
Solve:
$$x_{1} = -2$$
$$x_{2} = 4$$
$$x_{1} = -2$$
$$x_{2} = 4$$
This roots
$$x_{1} = -2$$
$$x_{2} = 4$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} < x_{1}$$
For example, let's take the point
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$-2 - \frac{1}{10}$$
=
$$- \frac{21}{10}$$
substitute to the expression
$$\sqrt{x^{2} - x - 1} > \sqrt{x + 7}$$
$$\sqrt{\left(-1\right) 1 - - \frac{21}{10} + \left(- \frac{21}{10}\right)^{2}} > \sqrt{- \frac{21}{10} + 7}$$
_____ ____ \/ 551 7*\/ 10 ------- > -------- 10 10
one of the solutions of our inequality is:
$$x < -2$$
_____ _____
\ /
-------ο-------ο-------
x_1 x_2Other solutions will get with the changeover to the next point
etc.
The answer:
$$x < -2$$
$$x > 4$$
Solving inequality on a graph
Rapid solution
[src]
Or(And(-7 <= x, x < -2), And(4 < x, x < oo))
$$\left(-7 \leq x \wedge x < -2\right) \vee \left(4 < x \wedge x < \infty\right)$$
((-7 <= x)∧(x < -2))∨((4 < x)∧(x < oo))
Rapid solution 2
[src]
[-7, -2) U (4, oo)
$$x\ in\ \left[-7, -2\right) \cup \left(4, \infty\right)$$
x in Union(Interval.Ropen(-7, -2), Interval.open(4, oo))