How to Find the Value of ab When a+b and a²+b² Are Given

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How to Find the Value of ab When


a+b and a²+b² Are Given

Content is

In algebra, many problems can be solved easily by using identities instead of lengthy calculations.

Let us see one such example.

Given:


a^2 + b^2 = 100 and a+b=12

We are asked to find the value of ab.

Step 1: Use the identity 

  (a+b)² = a² + b² + 2ab => (a+b)²  - 2ab = a² + b²

Step 2: Substitute the given values

   100 = (12)² -2ab => 100 = 144 - 2ab

Step 3: Solve for ab

    2ab = 144 - 100 => 2ab = 44 => ab = 22

Final Answer:  ab = 22


Conclusion:

Using algebraic identities helps us solve problems quickly and accurately. This method is very useful in exams and competitive tests.


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