Mathematics
Using (a - b)2 = (a2 + b2 - 2ab), evaluate:
(i) (97)2
(ii) (992)2
(iii) (9.98)2
Expansions
3 Likes
Answer
(i) Given,
⇒ (97)2
⇒ (100 - 3)2
Using identity :
⇒ (a - b)2 = a2 + b2 - 2ab
⇒ (100 - 3)2 = (100)2 + 32 - 2 × 100 × 3
⇒ (100 - 3)2 = 10000 + 9 - 600
⇒ 9409.
Hence, (97)2 = 9409.
(ii) Given,
⇒ (992)2
⇒ (1000 - 8)2
Using identity :
(a - b)2 = a2 + b2 - 2ab
⇒ (1000 - 8)2 = (1000)2 + 82 - 2 × 1000 × 8
⇒ (1000 - 8)2 = 1000000 + 64 - 16000
⇒ 984064.
Hence, (992)2 = 984064.
(iii) Given,
⇒ (9.98)2
⇒ (10 - 0.02)2
Using identity :
(a - b)2 = a2 + b2 - 2ab
⇒ (10 - 0.02)2 = (10)2 + 0.022 - 2 × 10 × 0.02
⇒ (10 - 0.02)2 = 100 + 0.0004 - 0.4
⇒ 99.6004
Hence, (9.98)2 = 99.6004.
Answered By
3 Likes
Related Questions
If , where , find the values of:
(i)
(ii)
(iii)
(iv)
Using (a + b)2 = (a2 + b2 + 2ab), evaluate:
(i) (137)2
(ii) (1008)2
(iii) (11.6)2
Fill in the blanks to make the given expression a perfect square:
(i) 16a2 + 9b2 + …………..
(ii) 25a2 + 16b2 - …………..
(iii) 4a2 + 20ab + …………..
(iv) 9a2 - 24ab + …………..
If (a + b + c) = 14 and (a2 + b2 + c2) = 74, find the value of (ab + bc + ca).