[" 1.1) "(77+210+7a(2))/((2x)/(a)+(y)/(b)=2)],[(x)/(a)-(y)/(b)=4]

2(x/a)+(y/b)=2; (x/a)-(y/b)=4

If (x+iy)^(1/3)=a+ib,x,y,ab in R. Show that (x)/(a)+(y)/(b)=4(a^(2)-b^(2))( ii) (x)/(a)-(y)/(b)=2(a^(2)+b^(2))

Find each of the following products: (i) (x + 3) (x - 3) (ii) (2x + 5)(2x - 5) (ii) (8 + x)(8 - x) (iv) (7x + 11y) (7x - 11y) (v) (5x^(2) + (3)/(4) y^(2)) (5x^(2) - (3)/(4) y^(2)) (vi) ((4x)/(5) - (5y)/(3)) ((4x)/(5) + (5y)/(3)) (vii) (x + (1)/(x)) (x - (1)/(x)) (viii) ((1)/(x) + (1)/(y)) ((1)/(x) - (1)/(y)) (ix) (2a + (3)/(b)) (2a - (3)/(b))

The solution of (dy)/(dx)=(1)/(2x-y^(2)) is given by , (A) y=Ce^(-2x)+(1)/(4)x^(2)+(1)/(2)x+(1)/(4)," 4"(1)/(2)," (B) "x=Ce^(-y)+(1)/(4)y^(2)+(1)/(4)y+(1)/(2)," (C) "x=Ce^(y)+(1)/(4)y^(2)+y+(1)/(2)," (D) "x=Ce^(2y)+(1)/(2)y^(2)+(1)/(2)y+(1)/(4)

if (x_(1),x_(2))^(2)+(y_(1)-y_(2))^(2)=a^(2), (x_(2)-x_(3))^(2)+(y_(2)-y_(3))^(2)=b^(2) (x_(3)-x_(1))^(2)+(y_(3)-y_(1))^(2)=c^(2). where a,b,c are positive then prove that 4 |{:(x_(1),,y_(1),,1),(x_(2) ,,y_(2),,1),( x_(3),, y_(3),,1):}| = (a+b+c) (b+c-a) (c+a-b)(a+b-c)

if (x_(1)-x_(2))^(2)+(y_(1)-y_(2))^(2)=a^(2), (x_(2)-x_(3))^(2)+(y_(2)-y_(3))^(2)=b^(2) (x_(3)-x_(1))^(2)+(y_(3)-y_(1))^(2)=c^(2). where a,b,c are positive then prove that 4 |{:(x_(1),,y_(1),,1),(x_(2) ,,y_(2),,1),( x_(3),, y_(3),,1):}| = (a+b+c) (b+c-a) (c+a-b)(a+b-c)

if (x_(1),x_(2))^(2)+(y_(1)-y_(2))^(2)=a^(2), (x_(2)-x_(3))^(2)+(y_(2)-y_(3))^(2)=b^(2) (x_(3)-x_(1))^(2)+(y_(3)-y_(1))^(2)=c^(2). where a,b,c are positive then prove that 4 |{:(x_(1),,y_(1),,1),(x_(2) ,,y_(2),,1),( x_(3),, y_(3),,1):}| = (a+b+c) (b+c-a) (c+a-b)(a+b-c)

Use a suitable identity to get each of the following products. (i) (x+3)(x+3) (ii) (2y+5)(2y+5) (iii) (2a-7)(2a-7) (iv) ((3a)-1/2)((3a)-1/2) (v) (1.1m-0.4)(1.1m+04) (vi) (a^2+b^2)(-a^2+b^2) (viI) (6x-7)(6x+7) (vii) (-a+c)(-a+c) (viii) (x/2+(3y)/4)(x/2+((3y)/4) (ix) (7a-9b)(7a-9b)

Use a suitable identity to get each of the following products. (i) (x+3)(x+3) (ii) (2y+5)(2y+5) (iii) (2a-7)(2a-7) (iv) ((3a)-1/2)((3a)-1/2) (v) (1.1m-0.4)(1.1m+04) (vi) (a^2+b^2)(-a^2+b^2) (viI) (6x-7)(6x+7) (vii) (-a+c)(-a+c) (viii) (x/2+(3y)/4)(x/2+((3y)/4) (ix) (7a-9b)(7a-9b)

Factorize each of the following algebraic expressions: (1) (x-y)^2+(x-y) (2) 6(a+2b)-4(a+2b)^2 (3) a(x-y)+2b(y-x)+c(x-y)^2 (4) -4\ (x-2y)^2+8(x-2y)