Question

if a+b=0.9 and ab=0.14,then the value of a-b and a²-b² is​

Answer 1

Answer:

• The value of a - b is 0.5.
• The value of a² - b² is 0.45.

Step-by-step explanation:

Given,

• a + b = 0.9
• ab = 0.14

To Find,

• The value of a - b.
• The value of a² - b².

Solution,

(a + b)² = a² + b² + 2ab

(a + b)² - 2ab = a² + b² •••[1]

(a - b)² = a² + b² - 2ab

(a - b)² + 2ab = a² + b² •••[2]

By adding Equation [1] and [2].

(a + b)² - 2ab = a² + b² = (a - b)² + 2ab

→ (a + b)² - 2ab = (a - b)² + 2ab

→ (a + b)² - 2ab - 2ab = (a - b)²

→ (a + b)² - 4ab = (a - b)²

→ (0.9)² - 4(0.14) = (a - b)²

[a + b = 0.9 , ab = 0.14]

→ 0.81 - 0.56 = (a - b)²

→ 0.25 = (a - b)²

→ (0.5)² = (a - b)²

→ a - b = 0.5

(a + b)(a - b) = a² - b²

[a + b = 0.9 , a - b = 0.5]

→ (0.9) × (0.5) = a² - b²

→ a² - b² = 0.45

Required Answer,

• a - b = 0.5
• a² - b² = 0.45