`5^(x)+3^(y)=14,5^(x-1)+3^(y-1)=4`

The value of (x , y) if 5^(x) + 3^(y) = 8,5^(x-1) + 3^(y-1) = 2 is :

(1)/(3)x+(1)/(4)y=4,(5)/(6)x-(1)/(8)y=4

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))

(14)/(x+y)+(3)/(x-y)=5,(21)/(x+y)-(2)/(x-y)=1

The image of the line (x-1)/3=(y-3)/1=(z-4)/(-5) in the plane 2x-y+z+3=0 is the line (1) (x+3)/3=(y-5)/1=(z-2)/(-5) (2) (x+3)/(-3)=(y-5)/(-1)=(z+2)/5 (3) (x-3)/3=(y+5)/1=(z-2)/(-5) (3) (x-3)/(-3)=(y+5)/(-1)=(z-2)/5

The image of the line (x-1)/(3)=(y-3)/(1)=(z-4)/(-5) in the plane 2x-y+z+3=0 is the line (1)(x+3)/(3)=(y-5)/(1)=(z-2)/(-5) (2) (x+3)/(-3)=(y-5)/(-1)=(z+2)/(5) (3) (x-3)/(3)=(y+5)/(1)=(z-2)/(-5) (3) (x-3)/(-3)=(y+5)/(-1)=(z-2)/(5)