Evaluate the following by using identity 1 (52 )²
Answers
Answer:
Evaluate using suitable identities :
(i) (52)²
Using the identity
=> (a+b)² = a² + 2ab + b²
(52)² = (50+2)²
= (50)² + 2×50×2 + (2)²
= 2500 + 200 + 4
= 2704
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(ii) (49)²
Using the identity
=> (a-b)² = a² - 2ab + b²
(49)² = (50 – 2)²
= (50)² - 2×50×1 + (1)²
= 2500 – 100 + 1
= 2401
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(iii) (103)²
Using the identity
=> (a+b)² = a² + 2ab + b²
(103)² = (100 + 3)²
= (100)² + 2×100×3 + (3)²
= 10000 + 600 + 9
= 10609
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(iv) (98)²
Using the identity
=> (a-b)² = a² - 2ab + b²
(98)² = (100 – 2)²
= (100)² - 2×100×2 + (2)²
= 10000 – 400 + 4
= 9604
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(v) (1005)²
Using the identity
=> (a+b)² = a² + 2ab + b²
(1005)² = (1000 + 5)²
= (1000)² + 2×1000×5 + (5)²
= 1000000 + 10000 + 25
= 1010025
Answer:
2704
Step-by-step explanation:
(52)²=(50+2)²
BY USING IDENTITY 1 :-
(a+b)²=a²+b²+2ab
∴(50+2)²=(50)²+(2)²+2(50) (2)
=2500+4+200
=2704
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