If `a ,b ,>0` such that `a^3+b^3=2,` then show that `a+blt=2.`

If a,b,quad >0 such that a^(3)+b^(3)=2, then show that a+b<=2.

If a, cgt0 such that a^3+b^3=2 , then show that a+ble 2 .

If a, bgt0 such that a^3+b^3=2 , then show that a+ble 2 .

If the line y=4x-5 touches the curve y^2 = a x^3 +b at point (2, 3) then show that 7a +2b=0.

If a + 2b + c= 0 , then show that: a^(3) + 8b^(3) + c^(3)= 6abc

If the acute angle between the lines ax^(2) + 2hxy + by^(2) = 0 is 60^(@) , then show that (a+3b)(3a+b) = 4h^(2) .

If the acute angle between the lines ax^(2) + 2hxy + by^(2) = 0 is 60^(@) , then show that (a+3b)(3a+b) = 4h^(2) .

If, for 0 lt a lt (1)/(2) , the sum of series a+a^(2) + a^(3)+… is b, then show that the series b - b^(2) + b^(3) - b^(4) +… is also convergent and hence find its sum.

If (a,0),(0,b) and (3,2) are collinear,show that 2a+3b-ab=0