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what is the value of ab if (a+b)²=36 and (a-b)²=24 ?

Hey Guys, hope you are well.


Today we are going to evaluate value of ab in a equation.

As you see in title,this equation is (a+b)²=36 and (a-b)²=24.


So if you love mathematics then you should read this article. To learn Algebra you should bookmark our site or you also follow us at SaRaisay.


Or guys,if you want read article in hindi language then visit our hindi Blog.


So, let's start.

What is the value of ab if (a+b)²=36 and (a-b)²=24 ?

what is the value of ab if (a+b)²=36 and (a-b)²=24 ?
            General Mathematics

I hope you are students.so you can learn with me.so let's start

METHOD 1:-

(a+b)²=36

That means (a+b)=√36
                                =6
So, a+b=6 
Hence a=6-b mark it as (I) 

(a-b)²=24 

That means (a-b)=√24
                               =2√6
So a-b=2√6
So now, putting the value of (I) of a

                    6-b-b=2√6
                        6-2b=2√6
                         2b=6-2√6
                           b=2(3-√6)/2
                            b=3-√6
Now putting the value of b in (I)
        a=6-3+√6=3+√6
  Therefore ab=(3-√6)(3+√6)    
                          =(3)² - (√6)²   [As we know
                           =9-6=3           (x+y)(x-y)=x²-y²]

Hence ab=3

Now,i know this is very long.We have to learn many things.so if you want any easy method then check this method below.

METHOD 2:-

(a+b)²=36

a²+2ab+b²=36  [(a+b)²=a²+2ab+b²] 
a²+2ab+b²=36...........(1)

(a-b)²=24 

a²-2ab+b²=24......….....(2)

Now substracting the two equation

(a²+2ab+b²)-(a²-2ab+b²)=36-24
a²+2ab+b²-a²+2ab-b²=12
           4ab=12     [a² and b² are removed because of 
              ab=12/4          opposite sign]
                   =3

Therefore ab equals to 3.

I hope you find it well.Here i tried to write from my best of my knowledge.

Read:-  Types of Roads।

So ,i believe that this article will help you lot.
So,from my side this is request to you if you love this article then please share with your friends and your classmates.

Thank you so much for reading this article.

Jai Hind...


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