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).
Given: a + b = 9 cm, a × b = 18 cm²
Formula Used: (a² – ab + b²) = (a + b)² - 3ab
Solution:
a + b = 9 cm and a × b = 18 cm².
(a² – ab + b²) = (a + b)² - 3ab,
(a + b)² = 9² = 81.
Now, (a² – ab + b²) = 81 - 3(18) = 81 - 54 = 27.
Thus, the value of (a² – ab + b²) is 27.
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