Question

Without actual calculations, find the value of:
i) 99
ii) 103 x 97

please tell me fast​

Answer 1

Answer:

I) (99)^2

= (90 + 9) ^2

= use identity 1

= (a +b)^2 = a^2 + b^2 + 2ab

= put the values

= (90)^2 + (9)^2 + 2 (90) (9)

= 8100 + 81 + 180× 9

=8100 +81 + 1620

= 9801 is the answer.

ii) 103 × 97

= (103) ^2 × (97)^2

= (100+ 3)^2 × (90 + 7) ^2

= use identity 1.

= (a+ b)^2 = a^2 + b^2 + 2ab

= [(100)^2 + (3)^2 + 2(100)(3)] × [(90)^2 + (7)^2 + 2(90)(7)]

= (10000+ 9+ 600) × (8100+ 49+ 12600)

=10609 × 20749

multiply it further

it'll surely help you