If x-y=2 and xy=15 find x square - y square and x cube - y cube - Maths - Polynomials

Question

If x-y=2 and xy=15 find x square - y square and x cube - y cube

Manbar Singh · Accepted Answer

We have,    x - y = 2⇒x-y2 = 4⇒x2 + y2 - 2xy = 4⇒x2+y2-30 = 4⇒x2+y2 = 34squaring both sides, we get     x4+y4 + 2x2y2 = 1156⇒x4+y4 + 2×225 = 1156⇒x4+y4 = 706Now, x2-y22 = x4+y4 - 2x2y2⇒ x2-y22= 706 - 450⇒ x2-y22 = 256⇒x2-y2 = ±16Now, x - y = 2⇒x-y3 = 8⇒x3-y3-3xyx-y = 8⇒x3-y3 - 45×2 = 8⇒x3-y3 = 98