The value of the expression (1.55² + 0.55² + 1.55 × 0.55) is equal to:

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Accepted Answer

We are given the expression: 1.55² + 0.55² + 1.55 × 0.55.

Let's denote a = 1.55 and b = 0.55.

Expression = a² + b² + ab.

Recall the identity for sum of cubes:
(a³ + b³) = (a + b)(a² - ab + b²).

We want to relate a² + b² + ab to something involving cubes.

Notice that:
(a + b)³ = a³ + b³ + 3ab(a + b)
=> a³ + b³ = (a + b)³ - 3ab(a + b)

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

Let's calculate the value numerically:

Calculate a² = (1.55)² = 2.4025
Calculate b² = (0.55)² = 0.3025
Calculate ab = 1.55 × 0.55 = 0.8525

Sum = 2.4025 + 0.3025 + 0.8525 = 3.5575

Calculate a³ = (1.55)³ = 1.55 × 1.55 × 1.55 = 3.723875
Calculate b³ = (0.55)³ = 0.166375
Sum of cubes = 3.723875 + 0.166375 = 3.89025

The value 3.5575 is close to but not equal to the sum of cubes 3.89025.

Check the options:
1) a² - b² = 2.4025 - 0.3025 = 2.1 (not equal)
2) a³ - b³ = 3.723875 - 0.166375 = 3.5575 (matches our expression value)
3) a³ + b³ = 3.89025 (not equal)
4) a² + b² = 2.705 (not equal)

So the expression equals a³ - b³.

Therefore, the correct option is 2: 1.55³ − 0.55³.

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