Question

Solve the following equations

(1) (x + 4) (x − 4) = 6x

(2) 2(a² − 1) = a(1 − a)

(3) 3(b − 5) (b − 7) = 4 (b + 3)

(4) 8(s − 1) (s + 1) + 2(s + 3) = 1

(5) (n − 3)² + (n + 1)² = 16

(6) 11(m + 1) (m + 2) = 38(m + 1) + 9m

Answer 1

(1)

The given equation can be reduced to an adfected quadratic equation as shown below.

Comparing the given equation with ,

Using the formula:

Hence, the roots of the quadratic equation are

(2)

The given equation can be reduced to an adfected quadratic equation as shown below.

Comparing the given equation with,

Using the formula:

Hence, the roots of the quadratic equation are

(3)

The given equation can be reduced to an adfected quadratic equation as shown below.

Comparing the given equation with _,

Using the formula_:

Hence, the roots of the quadratic equation are

(4)

The given equation can be reduced to an adfected quadratic equation as shown below.

Comparing the given equation with _,

Using the formula_:

Hence, the roots of the quadratic equation are

(5)

The given equation can be reduced to an adfected quadratic equation as shown below.

Hence, the roots of the quadratic equation are _.

(6)

The given equation can be reduced to an adfected quadratic equation as shown below.

Splitting the middle term, we get:

Hence, the roots of the quadratic equation are