Using identity, what is the value of ( 503^2+497^2 )?
Answer and explanation
Correct answer: 500018
Here, 503 = 500 + 3 and 497 = 500 - 3. Using the identity \((a+b)^2+(a-b)^2=2(a^2+b^2)\), we get \((503^2+497^2)=2(500^2+3^2)=2(250000+9)=500018\). The value 500000 includes only \(2\times500^2\); the term \(2\times3^2\) must also be added. Exam tip: When two numbers are equally spaced from a common middle number, use this identity for quick calculation.
Frequently asked questions
What is the correct answer to this question?
500018
Why is this the correct answer?
Here, 503 = 500 + 3 and 497 = 500 - 3. Using the identity \((a+b)^2+(a-b)^2=2(a^2+b^2)\), we get \((503^2+497^2)=2(500^2+3^2)=2(250000+9)=500018\). The value 500000 includes only \(2\times500^2\); the term \(2\times3^2\) must also be added. Exam tip: When two numbers are equally spaced from a common middle number, use this identity for quick calculation.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Exploring Algebraic Identities. Topic: Algebraic identities.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
