Question

[Tạ Thu Hương]

Tìm x, biết

a, 16x^2 - ( 4x-5)^2 = 15

b, (2x+3)^2 - 4(x-1)(x+1) = 49

c, (2x+1)(1-2x) + ( 1-2x)^3 =18

d, 2(x+1)^2 - ( x-3)(x+3) - (x

-4)^2 = 0

e, (x-5)^2 - x(x-4) = 9

f, ( x-5)^2 + ( x-4)(1-x) = 0

Giúp mk vs ạ mình đang cần

Answer 1

[Nguyễn Lê Phước Thịnh]

Tìm x

a) Ta có: \(16x^2-\left(4x-5\right)^2=15\)

\(\Leftrightarrow16x^2-\left(16x^2-40x+25\right)-15=0\)

\(\Leftrightarrow16x^2-16x^2+40x-25-15=0\)

\(\Leftrightarrow40x-40=0\)

\(\Leftrightarrow40x=40\)

hay x=1

Vậy: x=1

b) Ta có: \(\left(2x+3\right)^2-4\left(x-1\right)\left(x+1\right)=49\)

\(\Leftrightarrow4x^2+12x+9-4\left(x^2-1\right)-49=0\)

\(\Leftrightarrow4x^2+12x+9-4x^2+4-49=0\)

\(\Leftrightarrow12x-36=0\)

\(\Leftrightarrow12x=36\)

hay x=3

Vậy: x=3

d) Ta có: \(2\left(x+1\right)^2-\left(x-3\right)\left(x+3\right)-\left(x-4\right)^2=0\)

\(\Leftrightarrow2\left(x^2+2x+1\right)-\left(x^2-9\right)-\left(x^2-8x+16\right)=0\)

\(\Leftrightarrow2x^2+4x+2-x^2+9-x^2+8x-16=0\)

\(\Leftrightarrow12x-5=0\)

\(\Leftrightarrow12x=5\)

hay \(x=\frac{5}{12}\)

Vậy: \(x=\frac{5}{12}\)

e) Ta có: \(\left(x-5\right)^2-x\left(x-4\right)=9\)

\(\Leftrightarrow x^2-10x+25-x^2+4x-9=0\)

\(\Leftrightarrow-6x+16=0\)

\(\Leftrightarrow6x=16\)

hay \(x=\frac{8}{3}\)

Vậy: \(x=\frac{8}{3}\)

f) Ta có: \(\left(x-5\right)^2-\left(x-4\right)\left(1-x\right)=0\)

\(\Leftrightarrow x^2-10x+25-\left(x-x^2-4+4x\right)=0\)

\(\Leftrightarrow x^2-10x+25-x+x^2+4-4x=0\)

\(\Leftrightarrow2x^2-15x+29=0\)

\(\Leftrightarrow2\left(x^2-\frac{15}{2}x+\frac{29}{2}\right)=0\)

\(\Leftrightarrow x^2-2\cdot x\cdot\frac{15}{4}+\frac{225}{16}+\frac{7}{16}=0\)

\(\Leftrightarrow\left(x-\frac{15}{4}\right)^2+\frac{7}{16}=0\)(vô lý)

Vậy: x∈∅