find the value of: (optional)
i) 4x² + 25y² - 20xy when x=2 , y = -3
ii) x² + 1/x² , if x + 1/x = 6
iii) x² + 1/x² , if x - 1/x = 8
iv) x² + 4y² , if x + 2y = and xy =7
v) x - y , if x² + y² = 29 and xy = 2
(i) 4x2 +25y2 -20xy ;x=2,y=3
= 4*2*2 +25*3*3 -20*2*3
= 16 + 225 -60
= 181
(ii) x2 +1/x2,if x+1/x=6
or,(x+1/x)2 = x2 +1/x2 +2
or, (6)2 = x2 + 1/x2 +2
or, 36-2 =x2 + 1/x2
or, 34 = x2 +1/x2
(iii) x2 + 1/x2 , if x-1/x=8
or,(x-1/x)2 = x2 +1/x2 -2
or,(8)2 = x2 +1/x2 -2
or, 64+2 = x2 +1/x2
or, 66 = x2 +1/x2
(iv)in this question you have not given the value of x+2y
(v) x-y ;if x2 +y2 and xy =2
or, (x-y)2 = x2 + y2 -2xy
or,(x-y)2 = 29 -2*2
or,(x-y)2 = 29-4
or,(x-y)2 = 25
or, x-y =Square root of 25
or , x-y = -/+ 5
= 4*2*2 +25*3*3 -20*2*3
= 16 + 225 -60
= 181
(ii) x2 +1/x2,if x+1/x=6
or,(x+1/x)2 = x2 +1/x2 +2
or, (6)2 = x2 + 1/x2 +2
or, 36-2 =x2 + 1/x2
or, 34 = x2 +1/x2
(iii) x2 + 1/x2 , if x-1/x=8
or,(x-1/x)2 = x2 +1/x2 -2
or,(8)2 = x2 +1/x2 -2
or, 64+2 = x2 +1/x2
or, 66 = x2 +1/x2
(iv)in this question you have not given the value of x+2y
(v) x-y ;if x2 +y2 and xy =2
or, (x-y)2 = x2 + y2 -2xy
or,(x-y)2 = 29 -2*2
or,(x-y)2 = 29-4
or,(x-y)2 = 25
or, x-y =Square root of 25
or , x-y = -/+ 5