Question

Evaluate 5.9³ + 1.8³ + 4.8³ - 3 × 5.9 × 1.8 × 4.8 divided by 5.9² + 1.8² + 4.8² - (5.9 × 1.8) - (1.8 × 4.8) -(5.9 × 4.8)

Answer 1

Question :- Evaluate :- 5.9³ + 1.8³ + 4.8³ - 3 × 5.9 × 1.8 × 4.8 divided by 5.9² + 1.8² + 4.8² - (5.9 × 1.8) - (1.8 × 4.8) -(5.9 × 4.8)

Answer :-

we know that,

• a³ + b³ + c³ - 3abc = (a + b + c)(a² + b² + c² - ab - bc - ca)

taking :-

• a = 5.9
• b = 1.8
• c = 4.8

so, given expression can be written as :-

→ (5.9³ + 1.8³ + 4.8³ - 3 × 5.9 × 1.8 × 4.8) / {5.9² + 1.8² + 4.8² - (5.9 × 1.8) - (1.8 × 4.8) -(5.9 × 4.8)}

→ (a³ + b³ + c³ - 3abc) / (a² + b² + c² - ab - bc - ca)

Putting value of a³ + b³ + c³ - 3abc = (a + b + c)(a² + b² + c² - ab - bc - ca) in numerator we get,

→ (a + b + c)(a² + b² + c² - ab - bc - ca) / (a² + b² + c² - ab - bc - ca)

→ (a + b + c)

therefore,

→ 5.9 + 1.8 + 4.8

→ 12.5 (Ans.)

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if a^2+ab+b^2=25

b^2+bc+c^2=49

c^2+ca+a^2=64

Then, find the value of

(a+b+c)² - 100 = ...

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