প্রশ্ন:
A
- 2log
B
log2
C
2
D
- 1
উত্তরের বিবরণ
সমাধান:
0
Updated: 2 months ago
0
Updated: 2 months ago
3x + 4y = 7 এবং 4x - 3y = 1 হলে, x এর মান কত?
Created: 1 month ago
A
- 1
B
0
C
2
D
1
প্রশ্ন: 3x + 4y = 7 এবং 4x - 3y = 1 হলে, x এর মান কত?
সমাধান:
3x + 4y = 7......... (1)
4x - 3y = 1 ........ (2)
(1) কে 3 দিয়ে এবং (2) কে 4 দিয়ে গুণ করে যোগ করি,
3(3x + 4y) + 4(4x - 3y) = 3 × 7 + 4 × 1
⇒ 9x + 12y + 16x - 12y = 21 + 4
⇒ (9x + 16x) + (12y - 12y) = 25
⇒ 25x = 25
⇒ x = 25/25
∴ x = 1
0
Updated: 1 month ago
Created: 1 month ago
A
3
B
2
C
1
D
4
সমাধান:
a + (1/a) = 2
⇒ (a2 + 1)/a = 2
⇒ a2 + 1 = 2a
⇒ a2 - 2a + 1 = 0
⇒ (a - 1)2 = 0
⇒ a - 1= 0
∴ a = 1
এখন,
1/(a6 - a3 + 1) = 1/(16 - 13 + 1)
= 1/(1 - 1 + 1)
= 1/1
= 1
0
Updated: 1 month ago
x + y + z = 6 এবং x2 + y2 + z2 = 14 হলে, (x - y)2 + (y - z)2 + (z - x)2 এর মান কত?
Created: 3 weeks ago
A
4
B
5
C
6
D
7
প্রশ্ন: x + y + z = 6 এবং x2 + y2 + z2 = 14 হলে, (x - y)2 + (y - z)2 + (z - x)2 এর মান কত?
সমাধান:
(x - y)2 + (y - z)2 + (z - x)2
= x² - 2xy + y² + y² - 2yz + z² + z² - 2zx + x² [∵ (a - b)² = a² - 2ab + b²]
= 2x² + 2y² + 2z² - 2xy - 2yz - 2zx
= 2(x² + y² + z²) - 2(xy + yz + zx)
= 2 ⋅ 14 - 2(xy + yz + zx)
= 28 - {(x + y + z)² - (x² + y² + z²)} [∵ 2(ab + bc + ca) = (a + b + c)² - (a² + b² + c²)]
= 28 - (6² - 14)
= 28 - (36 - 14)
= 28 - 22
= 6
সমাধান:
(x - y)2 + (y - z)2 + (z - x)2
= x² - 2xy + y² + y² - 2yz + z² + z² - 2zx + x² [∵ (a - b)² = a² - 2ab + b²]
= 2x² + 2y² + 2z² - 2xy - 2yz - 2zx
= 2(x² + y² + z²) - 2(xy + yz + zx)
= 2 ⋅ 14 - 2(xy + yz + zx)
= 28 - {(x + y + z)² - (x² + y² + z²)} [∵ 2(ab + bc + ca) = (a + b + c)² - (a² + b² + c²)]
= 28 - (6² - 14)
= 28 - (36 - 14)
= 28 - 22
= 6
0
Updated: 3 weeks ago
