eva kiss

[eva kiss @hadassa200]

@BholanathDutta (8, 4, 7, 9):(8+9)-(4+7)=17-11=6
(4 & 7 → 7 - 4 = 3)

(9, X, 5, 1): (9+1)-(X+5)=3, 10-X-5=3, 5-X=3, X=2 (x=2, missing number)
(2 & 5 → 5 - 2 = 3)

(1, 3, 6, 8): (1+8)-(3+6)=9-9=0
(3 & 6 → 6 - 3 = 3)

[eva kiss @hadassa200]

@mathsrick_ X^x=2^√200
X^x=2^10√2
X^x=(2^5)^2√2
X^x=32^2√2
X^x=(32)^2√2(2/2)
X^x=(√32^2)^2√2
X^x=√32^4√2
X^x=(√32)^√16√2
X^x=√32^√32
X=√32=4√2

[eva kiss @hadassa200]

@IQTestBrain 2^t=t^32
2^1/32=t1/t
256^1/256 = t^1/t
t=256
(Check: 2^256=256^32, 2^256=2^8(32), 2^256=2^256)

[eva kiss @hadassa200]

@mathsrick_ x^√x=(√x)^x
x^√x=(x^1/2)^x
x^√x=x^x/2
√x=x/2
(√x)^2= (x/2)^2
x=x^2/4
x^2=4x
x^2-4x=0
x(x-4)=0, x=0, x-4=0, x=4
(Verify: √4^4=4^√4, 16=16)

[eva kiss @hadassa200]

@IQTestBrain 3^x+4^x=5^x
3^x/5^x +4^x/5^x=1
(3/5)^x+(4/5)^x=1
(3/5)^x+(4/5)^x=9/25+16/25
(3/5)^x=9/25, (3/5)^x=(3/5)^2, x=2
(4/5)^x=16/25, (4/5)^x=(4/5)^2, x=2
(Check: 3^2+4^2=5^2, 25=25)

[eva kiss @hadassa200]

@BholanathDutta (8,6): (8^2+6^2)/2=(64+36)/2=100/2=50
(5,7): (5^2+7^2)/2=(25+49)/2=74/2=37
(9,3): (9^2+3^2)/2= (81+9)/2=90/2=45
(4,6): (4^2+6^2)/2=(16+36)/2=52/2=26

[eva kiss @hadassa200]

@IQTestBrain 11+17=28
8+9=17
7+24=31 (missing number=C)
9+3=12

[eva kiss @hadassa200]

@mathsrick_ (x-1)^x = (5-1)^5, x=5
(Check: 4^5=4^5)

[eva kiss @hadassa200]

@mathsrick_ 2^√x/2-2^√y/2=504
Let: √x/2=m, √y/2=n, 2^m-2^n=504, 2^m>2^n, m>n
Let: m=k+n, 2^(k+n)-2^n=504, 2^n(2^k-1)=8(63)
2^n=2^3, n=3, 2^k-1=63, 2^k=2^6, k=6
m=k+n=3+6=9, m=9, (m,n)=(9,3)
Recall: m =√x/2, √x/2=9, x=18^2=324, x=324
n=√y/2, √y/2=3, y=6^2=36, y=36, (x,y)=(324,36)

[eva kiss @hadassa200]

@mathsrick_ 7^(-x+1) =4^(x-1)
7^-(x-1)/4^(x-1)=1
1/7^(x-1)4(x-1)=1
28^(x-1)=28^0
x-1=0
x=1

[eva kiss @hadassa200]

@mathsrick_ 3^x-3^y=6552
3^x>3^y, x>y
Let: x=y+k
3^(y+k)-3^y=6552
3^y(3^k-1)=9(728)
3^y=3^2, y=2
3^k-1=728, 3^k=729, 3^k=3^6, k=6
x=y+k=2+6=8, x=8, (x,y)=(8,2)
(Verify: 3^8-3^2=6552, 9(728)=6552, 6552=6552)

[eva kiss @hadassa200]

@BholanathDutta 111=21 ⇒ (1+1)(1x1)=21
222=44 ⇒ (2+2)(2x2)=44
223=46 ⇒ (2+2)(2x3)=46
334=612 ⇒ (3+3)(3x4)=612

[eva kiss @hadassa200]

@BholanathDutta (2+2)X2=08
(3+3)X3=18
(4+4)X4=32
(5+5)X5=50
(6+6)X6=72

[eva kiss @hadassa200]

@BholanathDutta (Vertically opposite angles)=75°
2X°=75°+85°=160°
X°=160/2=80°

[eva kiss @hadassa200]

@BholanathDutta (3x2)+4=6+4=10
(5x2)+3=10+3=13
(7x2)+2=14+2=16
(9x2)+3=18+3=21

[eva kiss @hadassa200]

@BholanathDutta (10,8): 10^2+8^2/2=100+64/2=164/2=82
(7,5): 7^2+5^2/2=49+25/2=74/2=37
(6,8): 6^2+8^2/2=36+64/2=100/2=50
(11,9): 11^2+9^2/2=121+81/2=202/2=101

[eva kiss @hadassa200]

@IQTestBrain 36x^3+324x^2+972x+972=x+2
36x^3+324x^2+971x+970=0
36x^3+120x^2+204x^2+680x+291x+970=0
(12.3)x^3+(12.10)x^2+(68.3)x^2+(68.10)x+(97.3)x+(97.10)=0
12x^2(3x+10)+ 68x(3x+10)+ 97(3x+10)=0
(3x+10)(12x^2+68x+97)=0, 3x+10=0, x1=-10/3= - 3 1/3 = -3.3, (Δ=-32 < 0) x2,3=-17/6±√2i/6

[eva kiss @hadassa200]

@mathsrick_ (x+1)^6=2^6
((x+1)^3)^2 –(2^3)^2=0
((x+1)^3 –2^3)((x+1)^3 +2^3)=0
Case1: (x+1)^3 –2^3=0, (x-1)(x^2+4x+7)=0
Case2: (x+1)^3 +2^3=0, (x+3)(x^2+3)=0
Case1: x1= 1, x^2+4x+7=0, Δ= -12 <0 no real solutions, x2,3 =-2±i√3
Case2: X4= -3, x^2+3=0, Δ=-12<0 no real solutions, x5,6 =±i√3

[eva kiss @hadassa200]

@mathsrick_ (y - 3)⁴- 5⁴ =0
((y-3)²)² - (5²)² =0
((y-3)² - 5²)((y-3)² + 5²)=0
Casei 1: (y-3)² - 5² =0, (y-8)(y+2)=0, Y1 =8, Y2 =-2
Casei 2: (y-3)² + 5²=0, y²-6y+34=0, y3,4 =3 ±i5
The real solutions to the equation are Y1 =8, Y2 =-2, while the complex solutions are y3,4 =3 ±i5

[eva kiss @hadassa200]

@BholanathDutta 5+3=28 ⇒ (5-3)(5+3)=28
9+1=810 ⇒ (9-1)(9+1)=810
8+6=214 ⇒ (8-6)(8+6)=214
5+4=19 ⇒ (5-4)(5+4)=19