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

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

If a, b, c and d are in proportion, then show that (a^(3)+3ab^(2))/(3a^(2)b+b^(3))=(c^(3)+3cd^(2))/(3c^(2)d+d^(3))

If a=3+2i,b=3-2i show that a^(2)+ab+b^(2)=23

If equations ax^(2)-bx+c=0 (where a,b,c epsilonR and a!=0 ) and x^(2)+2x+3=0 have a common root, then show that a:b:c=1:2:3

Let =|2a_1b_1a_1b_2+a_2b_1a_1b_3+a_3b_1a_1b_2+a_2b_1 2a_2b_2a_2b_3+a_3b_2a_1b_3+a_3b_1a_3b_2+a_2b_3 2a_3b_3| . Expressing as the product of two determinants, show that =0. Hence, show that if a x^2+2h x y+b y^2+2gx+2fy+c=(l x+m y+n)(l^(prime)x+m^(prime)y+n),t h e n|a hgh bfgfc|=0.

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

If A={1,2} and B={2,3} , then show that: AxxB ne B xxA

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 a^(3)-3a^(2)+5a-17=0 and b^(3)-3b^(2)+5b+11=0 are such that a+b is a real number, then the value of a+b is