Knowing a b 1, a 2 b 2 2, find a 7 b 7

a^3+b^3=(a+b)(a^2+b^2-ab)a^5+b^5=(a+b)^5-5ab[2ab(a+b)+a^3+b^3]

a^7+b^7=(a+b)^7-7ab[3ab(a^3+b^3)+(a^5+b^5)+5a^2b^2(a+b)]

Because. a+b=1

a 2 + b 2 = 2 = (a + b) 2-2ab so. 2=1-2ab

Get. ab=-1/2

Substitute a+b=1,a2+b 2=2,ab=-1 2 into the above formula.

In turn, we get: a 3 + b 3 = 5 2

a^5+b^5=19/4

a^7+b^7=71/8

Will ask for ab, right? ab=-1/2

Then calculate (a+b) 3*(a 2+b 2) 2, and then you can calculate all the items except a 7+b 7, and the answer is not difficult.

a+b=1,a^2+b^2=2

a+b)^2=a^2+b^2+2ab=1

2ab=-1

ab=-1/2

a, b Lenovo Vedic theorem.

Be. xx x 1 2 0 of 2 roots.

xx＝x＋1/2

aa=a+1/2

bb=b+1/2

a^n=a^(n-1)+(1/2)a^(n-2)b^n=b^(n-1)+(1/2)b^(n-2)s(n)=a^n+b^n

s(n-1)+(1/2)s(n-2)

s1=1s2=-1/2

s3=s1+1/2 s2=3/4

s4=s2+1/2 s3=-1/2+3/8=-1/8s5=s4+1/2 s3

s6=s5+1/2 s4

s7=s6+1/2(s5)

From a+b=1, a2+b2=2, ab=-1 2 can be obtained

Constructing the equation, a, b are the two roots of the equation 2x 2-x-4=0.

Even if it ends here, it won't be done.

a+b=1,(a+b) 2 =1,a 2 +b 2 +2ab=1 a 2 +b 2 =2,loss of filial piety 2+2ab=1,ab=,(a 2 +b 2 ) 2 =4, then there is a 4 +b 4 +2(ab) 2 =4,a 4 +b 4 =,squared:(a 4 +b 4 ) 2 =,a 8 +b 8 +2(ab) 4 =, Zhen Min.

A 8 +B 8 =, A 6 +B 6 = (A 2 +B 2) Written out [A 4 +B 4 -(AB) 2].

a 7 +b 7 =（a 7 +b 7 ）（a+b）a 8 +b 8 +ab 7 +ba 7

a 8 +b 8 ）+ab（a 6 +b 6 ）

Analysis: First write a2+b2 in the form of a perfect square formula, and then destroy a+b=7, ab=2 generations to guess

a2+b2=(a+b)2-2ab, a+b=7,ab=2 a2+b2=49-2 2=49-4=45 So the answer is 45

Comments: This question mainly examines the complete square formula, and it is very helpful to memorize several spike inspection and deformation formulas of the public sedan car style

Subtract the left from the left, and the right minus the right, and as a result, the left is 4ab, the right is 4, 4ab=4, and ab is equal to 1.