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ALGEBRA ALGEBRA b - Ce than b) + .* *exe i el (Formulae) b + (Dividing by x y z x² y ² 2² a = 3 yz (3)2 + 4 -9+4=13 b + - b a #V13 . (3) Cubing both sides, b 3 .. of =(113) Ole ole 33 + b +3x ba х ab =13/13 53 a3 + 19. If a + b + C=2s then find the value of (s-a) + (s - b)3 + 3 (s-a) (s - b) c (1) c (2) (4) 262 Sol. (3) a + b + c = 2s c=2s-a-b=(s-a) + (s-b) (s-a) + (s -b) + 3 (s-a) (s - b)c = (s-a)' + (s-b)3 + 3 (s-a)(s-b) Iſs- a) + (s- b)] (Put the value of c) = [(s-a) + (s- b)3 = (2s-a-b)3 (a + b + c-a-b)3 = < (Put the value of 2s) 20. If x + y + z = 10, x2 + y2 + 22 - 30, then find the value of x2 + y2 + 2 - 3xyz. (1) 50 (2) -50 (3) 40 (4) 40 Sol. (2) : *** 13 + 73 -3.xyz= (x + y + 2) (x2 + y2 + 72- - yz - zx - Formula We do not know the value of xy + y2 + 2x. First find it. .: (x + y + 2)= x2 + y2 + Z2 + 2 (xy + y2 + zx) Formula (102 = 30 +2 (xy + y2 + 2x) = 2 (xy + y2 + 2x) = 100 - 30 = 70 +3/13 =13/13 + = 13/13-31/13 1 10/13 16. If x + y + z = 15, XY + y2 + 2x=85, then find the value of x + y + 7. (1) 50 (2) 52 (3) 54 (4) 55 Sol. (4) : *+y+z= 15 Squaring both sides, . 70 - 35 ...
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