Question

please help me with these questions ​

Answer 1

AnsWer :

i)

• x = -2. and x = 5.

ii)

• x = 3/2 and x = -2.

iii)

• x = -5/√2 and x = -√2.

iv)

• x = 1/4 and x = 1/4

v)

• x = 1/10 and x = 1/10.

Solution :

Part ( iv )

We have equation,

$\tt\dagger \: \: \: \: \: 2 {x}^{2} - x + \dfrac{1}{8} = 0.$

$\tt \longmapsto \dfrac{16 {x}^{2} - 8x + 1}{8} = 0.$

$\tt \longmapsto {16x}^{2} - 8x + 1 = 0.$

Let's Compare with General Equation,

$\tt\dagger \: \: \: \: \: a {x}^{2} + bx + c = 0. \: \: \: \: \red{a \neq0.}$

Where as,

• a = 16.
• b = -8.
• c = 1.

$\rule{90}1$

Now, Apply Splitting the Middle term.

$\tt \longmapsto {16x}^{2} - 8x + 1 = 0.$

$\begin{array}{r | l} 2 & 16 \\ \cline{2-2} 2 & 8 \\ \cline{2-2} 2 & 4 \\ \cline{2-2} 2 & 2 \\\cline{2-2} & 1 \\ \end{array}$

$\tt \longmapsto 16 {x}^{2} - 4x - 4x + 1 = 0.$

$\tt \longmapsto 4x(4x - 1) - 1(4x - 1) = 0.$

$\tt \longmapsto (4x - 1)(4x - 1) = 0.$

$\rule{20}1$

Either,

$\tt \mapsto 4x - 1 = 0.$

$\tt\mapsto x = \dfrac{1}{4}$

$\rule{20}1$

Or,

$\tt \mapsto 4x - 1 = 0.$

$\tt\mapsto x = \dfrac{1}{4}$

$\rule{200}3$

Part ( v )

We have equation,

$\tt\dagger \: \: \: \: \: 100 {x}^{2} - 20x + 1 = 0$

Let's Compare with General Equation,

$\tt\dagger \: \: \: \: \: a {x}^{2} + bx + c = 0. \: \: \: \: \red{a \neq0.}$

Where as,

• a = 100.
• b = -20
• c = 1.

Now, Apply Splitting the Middle term.

$\tt\longmapsto 100 {x}^{2} - 20x + 1 = 0.$

$\begin{array}{r | l} 2 & 100 \\ \cline{2-2} 2 & 50 \\ \cline{2-2} 5 & 25 \\ \cline{2-2} 5 & 5 \\\cline{2-2} & 1 \\ \end{array}$

$\tt\longmapsto 100 {x}^{2} - 10x - 10x + 1 = 0.$

$\tt\longmapsto 10x(10 - 1) - 1(10 - 1) = 0.$

$\tt\longmapsto (10x - 1)(10x - 1) = 0.$

$\rule{20}1$

Either,

$\tt\mapsto 10x - 1 = 0.$

$\tt\mapsto x = \frac{1}{10}$

$\rule{20}1$

Or,

$\tt\mapsto 10x - 1 = 0.$

$\tt\mapsto x = \frac{1}{10}$

$\rule{200}3$

Note : All parts provide in attachment.