Advertisements
Advertisements
Question
The value of p for 512 – 492 = 100p is 2.
Options
True
False
Advertisements
Solution
This statement is True.
Explanation:
Solving for p,
(51)2 – (49)2 = 100p
⇒ (50 + 1)2 – (50 – 1)2 = 100p ...[∵ 51 = 50 + 1 and 49 = 50 – 1]
⇒ (2500 + 1 + 100) – (2500 + 1 – 100) = 100p ...[∵ (a + b)2 = a2 + b2 + 2ab and (a – b)2 = a2 + b2 – 2ab]
⇒ 2500 + 1 + 100 – 2500 – 1 + 100 = 100p
⇒ 200 = 100p
⇒ 100p = 200
⇒ p = `200/100` = 2
The value of p is 2.
APPEARS IN
RELATED QUESTIONS
(5 + 20)(–20 – 5) = ?
Find the value of (x – y)(x + y)(x2 + y2)
672 – 372 = (67 – 37) × ______ = ______.
The value of (a + 1)(a – 1)(a2 + 1) is a4 – 1.
Using suitable identities, evaluate the following.
(729)2 – (271)2
Factorise the following using the identity a2 – b2 = (a + b)(a – b).
`(2p^2)/25 - 32q^2`
Factorise the following using the identity a2 – b2 = (a + b)(a – b).
49x2 – 36y2
Factorise the following using the identity a2 – b2 = (a + b)(a – b).
`x^2/25 - 625`
Factorise the following using the identity a2 – b2 = (a + b)(a – b).
`(4x^2)/9 - (9y^2)/16`
Factorise the expression and divide them as directed:
(3x2 – 48) ÷ (x – 4)
