Practice set 4.3

 QUE (1) If ab= 73$\frac{\mathrm{<br>}}{}$ then find the values of the following ratios.

(i) 5a + 3b5a − 3b$\frac{\mathrm{.}}{}$  (ii) 2a2 + 3b22a2 − 3b2.   (iii)  a3 − b3b3.  (iv)  7a + 9b7a − 9b

ANSWER :

 Let's solve the question step by step using the given information and 

the calculated values of "a" and "b":

Given: ab = 73 ⇒ a^7 = b^3 = k ⇒ a = 7k, b = 3k

Solving the ratios:

(i) Ratio: (5a + 3b) / (5a - 3b)

Substitute a = 7k and b = 3k:

Ratio = (5a + 3b) / (5a - 3b) = (5 * 7k + 3 * 3k) / (5 * 7k - 3 * 3k)

= (35k + 9k) / (35k - 9k) = 44k / 26k = 22/13

(ii) Ratio: (2a^2 + 3b^2) / (2a^2 - 3b^2)

Substitute a = 7k and b = 3k:

Ratio = (2a^2 + 3b^2) / (2a^2 - 3b^2) = (2 * (7k)^2 + 3 * (3k)^2) / (2 * (7k)^2 - 3 * (3k)^2)

= (98k^2 + 27k^2) / (98k^2 - 27k^2) = 125k^2 / 71k^2 = 125 / 71

(iii) Ratio: (a^3 - b^3) / b^3

Substitute a = 7k and b = 3k:

Ratio = (a^3 - b^3) / b^3 = ((7k)^3 - (3k)^3) / (3k)^3

= (343k^3 - 27k^3) / 27k^3 = 316k^3 / 27k^3 = 316/27

(iv) Ratio: (7a + 9b) / (7a - 9b)

Substitute a = 7k and b = 3k:

Ratio = (7a + 9b) / (7a - 9b) = (7 * 7k + 9 * 3k) / (7 * 7k - 9 * 3k)

= (49k + 27k) / (49k - 27k) = 76k / 22k = 38/11

These are the simplified numerical values of the ratios based on 

the given values of "a" and "b."

QUE (2)

If 15a2 + 4b215a2 − 4b2 = 477 then find the values of the following ratios .

ANSWER :