Question

Tìm x :

a, \(\overline{3x}+\overline{x3}=11\cdot11\)

b, \(\left(x+1\right)+\left(x+4\right)+\left(x+7\right)+...+\left(x+28\right)=195\)

c, \(\left(x-452\right)\cdot\text{a}=\overline{aaaa}\)

Answer 1

a, \(\overline{3x}+\overline{x3}=11\cdot11\)

\(\overline{3x}+\overline{x3}=121\)

\(33+\overline{xx}=121\)

\(\overline{xx}=121-33\)

\(\overline{xx}=88\)

\(\Rightarrow x=8\).

b, \(\left(x+1\right)+\left(x+4\right)+\left(x+7\right)+...+\left(x+28\right)=195\)

1 + 4 + 7 + ... +28 là dãy số cách đều

Số số hạng : (28 - 1) : 3 + 1 = 10 (số)

Tổng dãy số : \(\dfrac{\left(28+1\right)\cdot10}{2}=145\)

Để tìm x, ta có :

\(x\cdot10+145=195\)

\(x\cdot10=195-145\)

\(x\cdot10=50\Rightarrow x=5\)

c, \(\left(x-452\right)\cdot\text{a}=\overline{aaaa}\)

\(x-452=\overline{aaaa}:a\)

\(x-452=1111\)

\(x=1111+452=1563\)