Question

若a平方+b平方=1,ab=12/25,则a三次方减b三次方=?a四次方减b四次方=?a六次方减b六

Answer 1

a²+b²=1

ab=12/25

(a-b)²=a²+b²-2ab

=1-2×12/25

=1/25

a-b=±1/5

(a+b)²=a²+b²+2ab

=1+2×12/25

=49/25

a+b=±7/5

a³-b³=(a-b)(a²+ab+b²)

=±1/5×(1+12/25)

=±37/125

a^4-b^4

=(a-b)(a+b)(a²+b²)

=±1/5*(±7/5)*1

=±7/25

a^6-b^6

=(a^3-b^3)(a^3+b^3)

=±37/125*(a+b)(a²-ab+b²)

=±37/125*(±7/5)*(1-12/25)

=±37/125*(±7/5)*13/25

=±3367/15625