In a rectangular field, the sum of the length and the breadth is 9 cm and the area is 18 cm². If the length is 'a' and breadth is 'b', then find the value of (a² - ab + b²).

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Accepted Answer

Given: a + b = 9 and ab = 18
We need to find a² - ab + b².

Step 1: Recall the identity:
(a - b)² = a² - 2ab + b²

Step 2: Express a² - ab + b² in terms of (a + b)² and ab:
(a + b)² = a² + 2ab + b²
=> a² + b² = (a + b)² - 2ab

So,
a² - ab + b² = (a² + b²) - ab = [(a + b)² - 2ab] - ab = (a + b)² - 3ab

Step 3: Substitute the given values:
(a + b)² = 9² = 81
ab = 18

Therefore,
a² - ab + b² = 81 - 3*18 = 81 - 54 = 27

Step 4: Check the options. 27 is option 4.

Correction: The calculation shows 27, but option 4 is 27, so the correct answer is 27.

Hence, the value of (a² - ab + b²) is 27.

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