Question

if the sum of two numbers is 11 and sum of their cubes is 737, find the sum of their squares

Answer 1

it's answer will be 85

because, 9 and 2 are the only no.

which addition of cube making 737 that's why sum of square is 85

Answer 2

Answer: 85

Step-by-step explanation: Let the numbers be a and b

∴  a  + b = 11        ······   eq 1

∴ $a^{3}$ + $b^{3}$ = 737     ·······  eq 2

from eq 1,

a = 11-b    ······   eq 3

from eq 2

(11-b)^{3}  + b^3 = 737

⇒ 11³ -3(11)²b +3(11)b² - b³ + b³ = 737

⇒1331 - 363b + 33b² = 737

⇒33b² -363b +1331 -737 = 0

⇒33b²-363b +594=0

⇒33(b² - 11b + 18) = 0

⇒b² - 11b + 18 = 0

⇒b² - 9b -2b +18 = 0

⇒b(b-9)-2(b-9)= 0

⇒(b-9)(b-2)= 0

∴ b= 9 or 2

from eq 3

a = 11- 9 {when b= 9}

  = 2

or

a = 11- 2 {when b = 2}

  = 9

∴ 2² + 9² = 85

or

9²+2² = 85