if a+b =10 and a^2 + b^2 =58 find the value of a^3 +b^3

Hello student,
Please find the answer to your question below
a³ + b³ = (a + b) (a² - ab + b²)
= 10 (58 - ab)
But (a + b)² = a² + 2ab + b² = 58+2ab
also (a+b)²=10² = 100 since a+b=10
58+2ab=100
=> 2ab =100-58=42
=> ab = 21
=>a³ + b³ = (a + b) (a² - ab + b²)
= 10 (58 - ab)
=10*(58 - 21) = 370

(a+b)^2=a^2+2ab+b^2 10^2=58+2ab (given:a^2+b^2=58)2ab=100-58ab=42÷2=21 (bringing 2 from oppsite) (a+b)^3=a+b(a^2-ab+b^2) (its the equa.)(a+b)^3=10(58-21) =370

If a+b=10 and a^2+b^2=58Then a^2+b^2=(a+b)^2-2.a.b→58=10^2-2.a.b→58=100-2.a.b→2.a.b=100-58→a.b= 42/2 =21a^3+b^3=(a+b)^3-3.a.b(a+b)=1000-630=-370 ans