(i) If 10^3 = a^2 – b^2, then a – b = (a) 5 (b) 0 (c) 10 (d) 15

Question

Read the passage and answer the questions that follow.

• An odd integer is the difference of two squares of integers.

• The cube of an integer is difference of two squares.

• The cube of an odd integer can be expressed as difference of two squares in two different ways.

• The difference of the cubes of two consecutive integers is difference of two squares.

(i) If 10³ = a² – b², then a – b =

(a) 5
(b) 0
(c) 10
(d) 15

(ii) If 9³ = a² – b² = c² – d², a + b + c + d =

(a) 720
(b) 750
(c) 800
(d) 810

(iii) 15³ – 14³ = a² – b², ab =

(a) 90000
(b) 95940
(c) 99550
(d) 99540

Answer 1

(i) (c) 10

(ii) (d) 810

(iii) (d) 99540