
How many real solutions does the equation has?
A) 3
B) 5
C) 7
D) 1
Answer
497.4k+ views
2 likes
Hint:
Here to solve this problem, we will first differentiate the equation and we will check whether this function is increasing or decreasing. If the differentiation of the equation is greater than zero then it will be increasing function otherwise decreasing function.
Complete step by step solution:
Let’s first consider the given equation as-
Now, we will differentiate the given equation with respect to on both sides.
Differentiating both the side, we get
As the exponents are even so even if we put a negative number, the result will be always greater than zero. So we can write,
Therefore, we can say that the function is a strictly increasing function. So, it will cut the axis at only one point and has only one real solution.
Hence, the number of real solutions of the equation is one.
Note:
We need to know the important properties of functions that we have used here.
Functions are said to be strictly increasing functions if the value of is greater than zero.
Functions are said to be strictly decreasing functions if the value of is less than zero.
Here we have also obtained the derivative of a function, which measures the rate of change of one variable with respect to the change of another variable.
Here to solve this problem, we will first differentiate the equation and we will check whether this function is increasing or decreasing. If the differentiation of the equation is greater than zero then it will be increasing function otherwise decreasing function.
Complete step by step solution:
Let’s first consider the given equation as-
Now, we will differentiate the given equation with respect to
Differentiating both the side, we get
As the exponents are even so even if we put a negative number, the result will be always greater than zero. So we can write,
Therefore, we can say that the function is a strictly increasing function. So, it will cut the axis at only one point and has only one real solution.
Hence, the number of real solutions of the equation
Note:
We need to know the important properties of functions that we have used here.
Functions are said to be strictly increasing functions if the value of
Functions are said to be strictly decreasing functions if the value of
Here we have also obtained the derivative of a function, which measures the rate of change of one variable with respect to the change of another variable.
Latest Vedantu courses for you
Grade 11 Science PCM | CBSE | SCHOOL | English
CBSE (2025-26)
School Full course for CBSE students
₹41,848 per year
Recently Updated Pages
Master Class 12 Business Studies: Engaging Questions & Answers for Success

Master Class 11 Accountancy: Engaging Questions & Answers for Success

Master Class 11 Social Science: Engaging Questions & Answers for Success

Master Class 11 Economics: Engaging Questions & Answers for Success

Master Class 11 Physics: Engaging Questions & Answers for Success

Master Class 11 Biology: Engaging Questions & Answers for Success

Trending doubts
Father of Indian ecology is a Prof R Misra b GS Puri class 12 biology CBSE

Who is considered as the Father of Ecology in India class 12 biology CBSE

Enzymes with heme as prosthetic group are a Catalase class 12 biology CBSE

A deep narrow valley with steep sides formed as a result class 12 biology CBSE

An example of ex situ conservation is a Sacred grove class 12 biology CBSE

Why is insulin not administered orally to a diabetic class 12 biology CBSE
