Prove that (ab+xy) (ax+by) `gt ` 4abxy, a,b,x, y `gt 0`

Prove that In (1 + x) lt "x for x" gt 0

Prove that ((n+1)/(2))^(n) gt (n!)

A function f: RrarrR satisfies the equation f(x) f(y) - f(xy) = x+ y, AAx,y in R and f(1) gt 0 , then

Solve graphically 2x - 3y gt 6

Solve the following system of inequalities graphically x + y gt 4, 2x - y gt 0

Prove that b^(2)c^(2) + c^(2)a^(2) + a^(2) b^(2) gt abc (a+b+c)

If x + y + z = 0 , prove that |(ax,by,cz),(cy,az,bx),(bz,cx,ay)|=xyz|(a,b,c),(c,a,b),(b,c,a)|

The area of the region bounded by y^(2) =4ax and x^(2) = 4ay , a gt 0 in sq. unit, is : a) 16(a^(2))/(3) b) 14 (a^(2))/(3) c) 13 (a^(2))/(3) d) 16 a^(2)