# If ${a^b} = 4 - ab$ and ${b^a} = 1$, where a and are b positive integers, find a.

$

{\text{A}}{\text{. 0}} \\

{\text{B}}{\text{. 1}} \\

{\text{C}}{\text{. 2}} \\

{\text{D}}{\text{. 3}} \\

$

Last updated date: 27th Mar 2023

•

Total views: 311.1k

•

Views today: 5.87k

Answer

Verified

311.1k+ views

Hint- A number of the form ${b^a}$ can be equal to one only if either b = 1 or a = 0.

In this question we have been given ${a^b} = 4 - ab$ and ${b^a} = 1$

And we know that ${b^a}$ can be equal to one only if either $b = 1$ or $a = 0$.

But we are given that $a$ and are $b$ positive integers

So, $a \ne 0$ $ \Rightarrow b = 1$

Now if we put $b = 1$ in the equation ${a^b} = 4 - ab$

We get,

${a^1} = 4 - a\left( 1 \right)$

$ \Rightarrow 2a = 4$

So, $a = 2$

Here the correct answer is option (C).

Note- In these types of questions, the most important part is the domain of our variables, most of us miss this point and get struck as they give two answers. So, all the given constraints should be taken into consideration while solving the question.

In this question we have been given ${a^b} = 4 - ab$ and ${b^a} = 1$

And we know that ${b^a}$ can be equal to one only if either $b = 1$ or $a = 0$.

But we are given that $a$ and are $b$ positive integers

So, $a \ne 0$ $ \Rightarrow b = 1$

Now if we put $b = 1$ in the equation ${a^b} = 4 - ab$

We get,

${a^1} = 4 - a\left( 1 \right)$

$ \Rightarrow 2a = 4$

So, $a = 2$

Here the correct answer is option (C).

Note- In these types of questions, the most important part is the domain of our variables, most of us miss this point and get struck as they give two answers. So, all the given constraints should be taken into consideration while solving the question.

Recently Updated Pages

If abc are pthqth and rth terms of a GP then left fraccb class 11 maths JEE_Main

If the pthqth and rth term of a GP are abc respectively class 11 maths JEE_Main

If abcdare any four consecutive coefficients of any class 11 maths JEE_Main

If A1A2 are the two AMs between two numbers a and b class 11 maths JEE_Main

If pthqthrth and sth terms of an AP be in GP then p class 11 maths JEE_Main

One root of the equation cos x x + frac12 0 lies in class 11 maths JEE_Main

Trending doubts

What was the capital of Kanishka A Mathura B Purushapura class 7 social studies CBSE

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Tropic of Cancer passes through how many states? Name them.

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

Name the Largest and the Smallest Cell in the Human Body ?