Question

Addition of two numbers is 34 and addition of square of both numbers is 650. Find the smallest number​

Answer 1

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Answer 2

Given:

a + b = 34---------(i)

a² + b² = 650-------(ii)

Now, According to Question

➟ (a + b)² = (34)²

➟ a² + b² + 2ab = 1156

Use the value of eq(ii)

➟ a² + b² + 2ab = 1156

➟ 650 + 2ab = 1156

➟ 2ab = 1156 - 650

➟ 2ab = 506---------(iii)

Now, subtract (iii) from (ii)

➟ (a² + b²) - (2ab) = (650) - (506)

➟ a² + b² - 2ab = 650 - 506

➟ (a - b)² = 144

On removing square

➟ a - b = √144

➟ a - b = 12-------------(iv)

On solving (i) & ((iv)

➟ (a + b) - (a - b) = 34 - 12

➟ a + b - a + b = 22

➟ 2b = 22

➟ b = 22/2

➟ b = 11

And

➟ a - b = 12

➟ a - 11 = 12

➟ a = 12 + 11

➟ a = 23

Therefore:-

The smallest number is 11.