(3/4)(5/6)(15/16）（24/25）…… (2003 / 2004) x ^ 2-2x-1 = 0. Find x ^ 4 + x ^ 3-5X ^ 2-7x + 5 If you add 100 and 168 to a positive integer, you can get two complete squares and find the positive integer

(3/4)(5/6)(15/16）（24/25）…… (2003 / 2004) x ^ 2-2x-1 = 0. Find x ^ 4 + x ^ 3-5X ^ 2-7x + 5 If you add 100 and 168 to a positive integer, you can get two complete squares and find the positive integer

X ^ 2-2x-1 = 0. Find x ^ 4 + x ^ 3-5X ^ 2-7x + 5
Original formula = x ^ 2 (x ^ 2-2x-1) + 3x (x ^ 2-2x-1) + 2 (x ^ 2-2x-1) + 7 = 7
If you add 100 and 168 to a positive integer, you can get two complete squares and find the positive integer
Let x, x + 168 = a * a, x + 100 = b * B
(a+b)(a-b)=68=17*4
A + B = 17, A-B = 4 or a + B = 34, A-B = 2 or a + B = 68, A-B = 1
Only a + B = 34 and A-B = 2 are consistent
a=18,b=16
x=156
So, this positive integer is 156

5-7X/6=3-5X/5=1

Does this equation hold?

4.86+(0.7x-3.5)=26.08-(1.5x+14.6)

The original formula = (0.7x-3.5) + (1.5x + 14.6) = 26.08-4.86
2.2x+11.1=21.22
2.2x=10.12
x=4.6

5/7x+6=4/5x-6

The original equation can be reduced to 5 / 7X + 12 = 4 / 5x
Namely: – 3 / 35x = – 12
∴x=140