Mangyaring lutasin q 69?

Sagot:

Ang sagot ay #option (2) #

Paliwanag:

Ang equation ay # x ^ 2-5x + 1 = 0 #

#=>#, # x ^ 2 + 1 = 5x #

Hatiin mo # x #

# x + 1 / x = 5 #……………………#(1)#

Square magkabilang panig

# (x + 1 / x) ^ 2 = 5 ^ 2 #

# x ^ 2 + 1 / x ^ 2 + 2 = 25 #

# x ^ 2 + 1 / x ^ 2 = 25-2 = 23 #…………………..#(2)#

Multiply #(1)# at #(2)#

# (x + 1 / x) (x ^ 2 + 1 / x ^ 2) = 23 * 5 = 115 #

# (x ^ 3 + 1 / x + x + 1 / x ^ 3) = 115 #

# x ^ 3 + 1 / x ^ 3 = 115-5 = 110 #…………………….#(3)#

Multiply #(2)# at #(3)#

# (x ^ 2 + 1 / x ^ 2) (x ^ 3 + 1 / x ^ 3) = 23 * 110 = 2530 #

# x ^ 5 + x + 1 / x + 1 / x ^ 3 = 2530 #

# x ^ 5 + 1 / x ^ 5 = 2530-5 = 2525 #

# (x ^ 10 + 1) / x ^ 5 = 2525 #

Ang sagot ay #option (2) #