If 7(a + b) = 343 and 7(a – b) = 16807, find the value of a and b.1.

1.	If 7(a + b) = 343 and 7(a – b) = 16807, find the value of a and b.1. 2, -42. 3, -43. 4, -14. 3, -1
Answer» Correct Answer - Option 3 : 4, -1 Given∶ 7^{(a + b)} = 343 and 7^{(a – b)} = 16807 Formula Used∶ Basic knowledge of cube and cube root, solution of linear equations in two variables Calculation∶ 7^{(a + b)} = 343 ⇒ 7^{(a + b)} = 7³ ⇒ a + b = 3……..…(1) ⇒ 7^{(a – b)} = 16807 ⇒ 7^{(a – b)} = 7⁵ ⇒ a – b = 5................(2) Add equation (1) and (2), we get a + b + a – b = 3 + 5 ⇒ 2a = 8 ⇒ a = 4 Put the value of 8 in equation (1) a + b = 3 ⇒ 4 + b = 3 ⇒ b = 3 – 4 ⇒ b = -1 ∴ The value of a is 4 and b is -1.

If 7(a + b) = 343 and 7(a – b) = 16807, find the value of a and b.1. 2, -42. 3, -43. 4, -14. 3, -1

Answer» Correct Answer - Option 3 : 4, -1

Given∶

7^{(a + b)} = 343 and 7^{(a – b)} = 16807

Formula Used∶

Basic knowledge of cube and cube root, solution of linear equations in two variables

Calculation∶

7^{(a + b)} = 343

⇒ 7^{(a + b)} = 7³

⇒ a + b = 3……..…(1)

⇒ 7^{(a – b)} = 16807

⇒ 7^{(a – b)} = 7⁵

⇒ a – b = 5................(2)

Add equation (1) and (2), we get

a + b + a – b = 3 + 5

⇒ 2a = 8

⇒ a = 4

Put the value of 8 in equation (1)

a + b = 3

⇒ 4 + b = 3

⇒ b = 3 – 4

⇒ b = -1

∴ The value of a is 4 and b is -1.