\(A=\left(a-b\right)^2=\left(a+b\right)^2-4ab=5^2-4.2=17\)
Lời giải:
$A=(a-b)^2=a^2-2ab+b^2=(a+b)^2-4ab=5^2-4.2=17$
\(\left(a-b\right)^2=\left(a+b\right)^2-4ab=5^2-4\cdot2=25-8=17\)
\(A=\left(a-b\right)^2=\left(a+b\right)^2-4ab=5^2-4.2=17\)
Lời giải:
$A=(a-b)^2=a^2-2ab+b^2=(a+b)^2-4ab=5^2-4.2=17$
\(\left(a-b\right)^2=\left(a+b\right)^2-4ab=5^2-4\cdot2=25-8=17\)
Cho a + b = 1. Tính A = 2\(\left(a^3+b^3\right)\) - 3\(\left(a^2+b^2\right)\).
Cho \(a+b=5,ab=-2\left(a< b\right)\). Hãy tính \(a^2+b^2,\dfrac{1}{a^3}+\dfrac{1}{b^3},a-b,a^3-b^3\)
Cho \(\left(a-b\right)^2+\left(b-c\right)^2+\left(c-a\right)^2=4.\left(a^2+b^2+c^2-ac-bc-ca\right)\). Chứng minh rằng : a = b = c
Cho a + b = 7, a.b = 10. Tính:
a, A = \(a^2+b^2\).
b, B = \(a^3+b^3\).
c, C = \(a^4+b^4\).
d, D = \(a^5+b^5\).
e, E = a - b.
Cho a,b,c thỏa mãn \(b\ne c,a+b\ne c,c^2=2\left(ac+bc-ab\right)\)
C/m:
\(\dfrac{a^2+\left(a-c\right)^2}{b^2+\left(b-c\right)^2}=\dfrac{a-c}{b-c}\)
chứng minh các đẳng thức sau
a)\(\left(a+b+c\right)^2+\left(b+c-a\right)^2\left(c+a-b\right)^2\left(a+b+c\right)^2=4\left(a^2+b^2+c^2\right)\)
b) \(\left(a+b+c+d\right)^2+\left(a+b-c-d\right)^2+\left(a+c-b-d\right)^2+\left(a+d-b-c\right)^2=4\left(a^2+b^2+c^2+d^2\right)\)
Tìm x, biết:
a) \(\left(x+5\right)^2-\left(x+5\right)\left(x-5\right)\)
b) \(2x^2-x-1=0\)
Cho a + b + c = 0. Chứng minh rằng: \(a^3+b^3+c^3=3abc\)
Câu 1: Phân tích thành nhân tử:
\(\text{a) }a\left(a+2b\right)^3-b\left(2a+b\right)^3\)
\(\text{b) }\left(a+b\right)\left(a^2-b^2\right)+\left(b+c\right)\left(b^2-c^2\right)\left(c+a\right)\left(c^2-a^2\right)\)
Câu 2: Cho \(a^3+b^3+c^3-3abc=0\)
Chứng minh: \(a=b=c\)
Cho \(2\left(a^2+b^2\right)=\left(a+b\right)^2\) . Chứng minh : a = b