Solution plzz

Any no. Or its sum of digits divided by 9 gives same remainder so
2²+4²+6²+8²+.......98²
2²(1²+2²+3²+.......+49²)
4*(49*50*99/6)=> 161700
161700/9=> sum of digit = 6
So Ans =>6

It's sir Ramanujan series ....


3=√9
= √1+8
=√1+2√16
=√1+2√1+3√25
=√1+2√1+3√1+4√36
=>>>>> So on

3=>√1+2√1+3√1+4√1+5√........

x^3+y^2+3xy=125
27x^2y+27x^3+9xy^2+y^3=0

(3x+y)^3=0 => y=-3x
x^3+y^2+3xy=125
x^3+9x^2-9x^2=125

=> x^3=125; x=5
=> y=-3x; y=-15

x+y=-10 ✅

sqrt(1+2sqrt(1+....)=x

x^2=1+2sqrt(1+....)
x^2-1=2sqrt(1+3sqrt(1+....)
(x-1)(x+1)=2sqrt(1+3sqrt(1+....)


(x-1)(x+1)=(x-1)•sqrt(x^2+2x+1)=
(x-1)•sqrt(1+x(x+2))=
(x-1)•sqrt(1+x•sqrt(x^2+4x+4))=
(x-1)•sqrt(1+x•sqrt(1+(x+1)(x+3))=....


(x-1)•sqrt(1+x•sqrt(1+..)=2sqrt(1+....)

x-1=2 => x=3 ✅

20/21

Area of DEF = {2abc/(a+b)(b+c)(c+a) } * A

=>2*60*6/(7*9*8)=10/7

So
3=====10/7
2====20/21

Solve it

81x^4+1/x^4=(9x^2+1/x^2)^2-18=3007
9x^2+1/x^2=55
(3x-1/x)^2+2•3=55
3x-1/x=7
3x^2-7x=1
36x^2-84x=12

(6x-7)^2=36x^2-84x+49=12+49=61✅

x^3=a+sqrt(a^2+b^3)+a-sqrt(a^2+b^3)
+3(a^2-a^2-b^3)^1/3•x

x^3=2a-3bx
x^3+3bx=2a

Let f(x)=xsinx+(25/xsinx)
0<sinx<1
X€(0,π/2). Xsinx>0
Am>=Gm
F(x)/2>=√25)
F(x)>=10