Question

if x+y=7 and xy=12 find the value of (x^2-xy+y^2)​

Answer 1

Answer:

x²-xy+y² = 13

given: x + y = 7 and xy = 12

to evaluate x² - xy + y²

Step-by-step explanation:

(x + y)³ = 7³ = x³ + y³ + 3xy(x+y) [ identity ]

=> 343 = x³ + y³ + 3*12(7)

=> 343 = x³ + y³ + 252

=> x³ + y³ = 343 - 252

=> x³ + y³ = 91............1

now, x³ + y³ = (x+y)(x²-xy+y²) [identity ]

91 = 7 ( x²-xy+y²)

therefore x²-xy+y² = 91/7 = 13