Question

If x - y =7 and x³ - y³ = 133 find: (i) xy (ii) x² + y²​

Answer 1

Answer:

Step-by-step explanation:

wnswer

$x^3-y^3=(x-y)(x^2+y^2+xy)$

x-y=7

$(x-y)^2=x^2+y^2-2xy$

49=$x^2+y^2-2xy$

$x^2+y^2=49+2xy$.........eq1

$x^3-y^3=(x-y)(x^2+y^2+xy)$

133=7(49+2xy+xy)

19=49+3xy

-30=3xy

xy=-10......eq2

substitute eq2 in eq1

$x^2+y^2$=49-20=29