Question
Factorise:
$\text{x}^4+\frac{4}{\text{x}^4}$
$\text{x}^4+\frac{4}{\text{x}^4}$
✓
Answer
$\text{x}^4+\frac{4}{\text{x}^4}$
$=\text{x}^4+\frac{4}{\text{x}^4}+4-4$
$=\big(\text{x}^2\big)^2+\Big(\frac{2}{\text{x}^2}\Big)^2+2\big(\text{x}^2\big)\Big(\frac{2}{\text{x}^2}\Big)-2^2$
$=\bigg[\big(\text{x}^2\big)^2+\Big(\frac{2}{\text{x}^2}\Big)^2+2\big(\text{x}^2\big)\Big(\frac{2}{\text{x}^2}\Big)\bigg]-2^2$
$=\Big[\text{x}^2+\frac{2}{\text{x}^2}\Big]^2-2^2$
$=\Big(\text{x}^2+\frac{2}{\text{x}^2}+2\Big)\Big(\text{x}^2+\frac{2}{\text{x}^2}-2\Big)$
$=\text{x}^4+\frac{4}{\text{x}^4}+4-4$
$=\big(\text{x}^2\big)^2+\Big(\frac{2}{\text{x}^2}\Big)^2+2\big(\text{x}^2\big)\Big(\frac{2}{\text{x}^2}\Big)-2^2$
$=\bigg[\big(\text{x}^2\big)^2+\Big(\frac{2}{\text{x}^2}\Big)^2+2\big(\text{x}^2\big)\Big(\frac{2}{\text{x}^2}\Big)\bigg]-2^2$
$=\Big[\text{x}^2+\frac{2}{\text{x}^2}\Big]^2-2^2$
$=\Big(\text{x}^2+\frac{2}{\text{x}^2}+2\Big)\Big(\text{x}^2+\frac{2}{\text{x}^2}-2\Big)$
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Read the Source/ Text given below and answer these questions:
There is a square park ABCD in the middle of Saket colony in Delhi. Four children Deepak, Ashok, Arjun and Deepa went to play with their balls. The colour of the ball of Ashok, Deepak, Arjun and Deepa are red, blue, yellow and green respectively. All four children roll their ball from centre point O in the direction of XOY, X'OY, X'OY' and XOY'. Their balls stopped as shown in the above image.
questions:
1. What are the coordinates of the ball of Ashok?
2. What are the coordinates of the ball of Deepa?
There is a square park ABCD in the middle of Saket colony in Delhi. Four children Deepak, Ashok, Arjun and Deepa went to play with their balls. The colour of the ball of Ashok, Deepak, Arjun and Deepa are red, blue, yellow and green respectively. All four children roll their ball from centre point O in the direction of XOY, X'OY, X'OY' and XOY'. Their balls stopped as shown in the above image.
questions:
1. What are the coordinates of the ball of Ashok?
2. What are the coordinates of the ball of Deepa?