Solve the following equation and verify your answer: ( x+1 x-4 )^… - Vidyadip

Question

Solve the following equation and verify your answer: $\Big(\frac{\text{x}+1}{\text{x}-4}\Big)^2=\frac{\text{x}+8}{\text{x}-2}$

✓

Answer

$\Big(\frac{\text{x}+1}{\text{x}-4}\Big)^2=\frac{\text{x}+8}{\text{x}-2}$
$\Rightarrow\frac{(\text{x}+1)^2}{(\text{x}-4)^2}=\frac{(\text{x}+8)}{(\text{x}-2)}$
By cross multiplication, $=(\text{x}+1)^2(\text{x}-2)=(\text{x}-4)^2(\text{x}+8)$
$\Rightarrow(\text{x}^2+2\text{x}+1)(\text{x}-2)=(\text{x}^2-8\text{x}+16)(\text{x}+8)$
$\Rightarrow\text{x}^3-2\text{x}^2+2\text{x}^2-4\text{x}+\text{x}-2$
$=\text{x}^3+8\text{x}^2-8\text{x}^2-64\text{x}+16\text{x}+128$
$\Rightarrow\text{x}^3-3\text{x}-2=\text{x}^3-48\text{x}+128$
$\Rightarrow\text{x}^3 -3\text{x}-\text{x}^3+48\text{x}-128+2$ (By transposition)
$\Rightarrow45\text{x}$
$=130$
$\Rightarrow\text{x}=\frac{130}{45}$
$=\frac{26}{9}$
$\therefore\text{x}=\frac{26}{9}$
Verification: $\text{L.H.S}=\bigg(\frac{\text{x}+1}{\text{x}-4}\bigg)^2=\Bigg(\frac{\frac{26}{9}+1}{\frac{26}{9}-4}\Bigg)^2$
$=\Bigg(\frac{\frac{26+9}{9}}{\frac{26-36}{9}}\Bigg)^2=\Bigg(\frac{\frac{35}{9}}{\frac{-10}{9}}\Bigg)^2$
$=\bigg(\frac{35}{9}\times\frac{9}{-10}\bigg)^2=\bigg(\frac{-7}{2}\bigg)^2=\frac{49}{4}$
$\text{R.H.S}=\frac{\text{x}+8}{\text{x}-2}=\frac{\frac{26}{9}+8}{\frac{26}{9}-2}=\frac{\frac{26+72}{9}}{\frac{26-18}{9}}=\frac{\frac{98}{9}}{\frac{8}{9}}$
$=\frac{98}{9}\times\frac{9}{8}=\frac{49}{4}$
$\therefore\text{L.H.S}=\text{R.H.S}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "5 Marks Questions" from Linear Equations in One Variable→Linear Equations in One Variable — all question types→MATHS STD 8 question papers→Gujarat Board STD 8 question papers→Gujarat Board question paper generator→

Similar questions

The table shows the time four elevators take to travel various distances. Find which elevator is fastest and which is slowest.

	Distance (m)	Time (sec.)
Elevator $- A$	$435$	$29$
Elevator $- B$	$448$	$28$
Elevator $- C$	$130$	$10$
Elevator $- D$	$85$	$5$

How much distance will be travelled by elevators $B$ and $C$ seperately in $140$sec? Who travelled more and by how much?

Ravish has three boxes whose total weight is $60\frac{1}{2}$ $kg$. Box $B$ weighs $3\frac{1}{2}$ $kg$. more then box $A$ and box $C$ weighs $5\frac{1}{3}$ $kg$. more than box $B$. Find the weight of box $A$.

Construct a quadrilateral $\text{BEAR}$ in which $\text{BE} = 6\ cm, \text{EA} = 7\ cm, \text{RB = RE} = 5\ cm$ and $\text{BA} = 9\ cm$. Measure its fourth side.

Find product: $\big(\frac{1}{8}\text{x}^2\text{y}^4\big)×\big(\frac{1}{4}\text{x}^4\text{y}^2\big)×(\text{xy})×5$

Ashima sold two coolers for $Rs. 3,990$ each. On selling one cooler she gained $5\%$ and on selling the the other she suffered a loss of 5%. Find her overall gain or loss $\%$ in whole transaction.

Subtract the following polynomials :
$5 x^2 y+3 x y+4 y x^2-2 y^2 x$ from $x^2 y-x y+5 y x^2$

Resolve each of the following quadratic trinomial into factor:
$12x^2- 17xy + 6y^2$

The central hall of a school is $80m$ long and $8m$ high. It has $10$ doors each of size $3m \times 1.5m$ and $10$ windows each of size $1.5m \times l m$. If the cost of the white-washing the walls of the hall at the rate of $Rs. 1.20$ per $m^2$ is $Rs. 2385.60$, find the breadth of the hall.

Express product as a monomials and verify the result in each case for $x = 1$: $\big(4\text{x}^2\big) × (-3\text{x}) × \big(\frac{4}{5}\text{x}^3\big)$

The following table shows the percentage of students who dropped out of school after completing high school.

Year	$2005$	$2007$	$2009$	$2011$	$2013$	$2015$	$2017$
Percentage of students who dropped out of school	$6\%$	$5.5\%$	$5\%$	$4.7\%$	$4.9\%$	$4\%$	$4.5\%$

Study the above table carefully and draw a line graph to depict it.