What value is obtained by simplifying ( 51^2+49^2 ) using identity?
Answer and explanation
Correct answer: 5002
Here, \(51=50+1\) and \(49=50-1\). Using the identity \((a+b)^2+(a-b)^2=2a^2+2b^2\), with \(a=50\) and \(b=1\), we get \(51^2+49^2=2(50)^2+2(1)^2=5000+2=5002\). The value 5000 includes only \(2\times 50^2\); \(2\times 1^2\) must also be added. Exam tip: apply this identity directly when two numbers are equally spaced from a middle number.
Frequently asked questions
What is the correct answer to this question?
5002
Why is this the correct answer?
Here, \(51=50+1\) and \(49=50-1\). Using the identity \((a+b)^2+(a-b)^2=2a^2+2b^2\), with \(a=50\) and \(b=1\), we get \(51^2+49^2=2(50)^2+2(1)^2=5000+2=5002\). The value 5000 includes only \(2\times 50^2\); \(2\times 1^2\) must also be added. Exam tip: apply this identity directly when two numbers are equally spaced from a middle number.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Exploring Algebraic Identities. Topic: Algebraic identities.
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