If the square of a + the square of B = 25, ab = 12, find the square of a + B, A-B, a-b Given that 1 / 2 of x-x = 2, find (1) the square of X + 1 / 2 of X (2) the fourth power of X + 1E of X (3) x + 1 / 2 of X

If the square of a + the square of B = 25, ab = 12, find the square of a + B, A-B, a-b Given that 1 / 2 of x-x = 2, find (1) the square of X + 1 / 2 of X (2) the fourth power of X + 1E of X (3) x + 1 / 2 of X

one
(a+b)^2=a^2+b^2+2ab=25+24=49
A + B = 7 or - 7
two
(a-b)^2=a^2+b^2-2ab=25-24=11
A + B = radical 11 or - radical 11
three
A ^ 2-B ^ 2 = (a-b) (a + b) = 7 radical 11 or - 7 radical 11

Given the square of a + the square of B = 25, ab = - 12, find the square of (a-b)

Square of (a-b) = known square of a + square of B - 2Ab = 25-2 * (- 12) = 25 + 24 = 49

If the square of a + the square of B = 1, ab = 12 / 25, then a + B=__ ;
The third power of a - the third power of B =;
The fourth power of a - not the fourth power =;
The sixth power of a - the sixth power of B =;

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