Answer

Verified

409.5k+ views

**Hint:**An extraneous solution is a solution value of the variable in the equations, that is found by solving the given equation algebraically but it is not a solution of the given equation. We get these types of solutions sometimes when we solve radical equations. Radical equations are equations in which the variable is under a radical. To find the solution of a radical equation, we need to take the radical expression to one side of the equations. If there is more than one radical expression, take one at a time.

**Complete step by step answer:**

Let’s take an example of radical expression \[x+1=\sqrt{7x+15}\]. We need to solve this equation. Squaring both sides of the above equation, we get

\[\Rightarrow {{\left( x+1 \right)}^{2}}={{\left( \sqrt{7x+15} \right)}^{2}}\]

simplifying the above equation, we get

\[\begin{align}

& \Rightarrow {{x}^{2}}+2x+1=7x+15 \\

& \Rightarrow {{x}^{2}}-5x-14=0 \\

\end{align}\]

We can find the roots of the above quadratic equation, by using the formula method, as follows

\[\begin{align}

& \Rightarrow x=\dfrac{-(-5)\pm \sqrt{{{\left( -5 \right)}^{2}}-4(1)(-14)}}{2(1)} \\

& \Rightarrow x=\dfrac{5\pm \sqrt{81}}{2} \\

& \Rightarrow x=\dfrac{5\pm 9}{2} \\

\end{align}\]

\[\Rightarrow x=\dfrac{5+9}{2}=\dfrac{14}{2}\] or \[x=\dfrac{5-9}{2}=\dfrac{-4}{2}\]

\[\therefore x=7\] or \[x=-2\]

But if we substitute \[x=-2\] in the equation, we get

\[\begin{align}

& -2+1=\sqrt{7(-2)+15} \\

& \Rightarrow -1=1 \\

\end{align}\]

Which is not correct. Hence, \[x=-2\] is not a solution of the given radical equation. Thus \[x=-2\] is an extraneous solution for the given equation.

**Note:**We should know when an extraneous solution occurs. Extraneous solutions of an equation are solutions that occur when a radical expression that has an even index, such as 2, is raised to its power to find the solution of an equation.

In the above example, as the radical power has an even index, we get \[x=-2\] as an extraneous solution of the equation.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Mark and label the given geoinformation on the outline class 11 social science CBSE

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Trending doubts

Difference Between Plant Cell and Animal Cell

In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE

Which are the Top 10 Largest Countries of the World?

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

How do you graph the function fx 4x class 9 maths CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths