Question : If x + y = √3 and x – y = √2, the value of 8xy(x2 + y2) is:
Option 1: 6
Option 2: √6
Option 3: 5
Option 4: √5
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Correct Answer: 5
Solution :
According to the question,
x + y = √3
Squaring both sides, we get,
⇒ x
2
+ y
2
+ 2xy = 3 ––––––––––––(i)
Now, x – y = √2
Squaring both sides, we get,
⇒ x
2
+ y
2
– 2xy = 2 ––––––––––––(ii)
Adding equations (i) and (ii), we get,
2x
2
+ 2y
2
= 5
⇒ x
2
+ y
2
= $\frac{5}{2}$ ––––––––––––––––(iii)
Now putting the value from equation (iii) in equation (i), we get,
$\frac{5}{2}$ + 2xy = 3
⇒ 2xy = 3 – $\frac{5}{2}$
⇒ 2xy = $\frac{1}{2}$
$\therefore$ xy = $\frac{1}{4}$
Now, the value of 8xy(x
2
+ y
2
)
= $8 × \frac{1}{4} × \frac{5}{2}$
= $5$
Hence, the correct answer is 5.
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