If y = √8 + √7, then what is the value of y3 + (1/y3)?
A
116√2
B
81√2
C
64√3
D
34√2
উত্তরের বিবরণ
Solution:
দেওয়া আছে,
y = √8 + √7
⇒ 1/y = 1/(√8 + √7)
⇒ 1/y = (√8 - √7)/(√8 + √7)(√8 - √7)
⇒ 1/y = (√8 - √7)/{(√8)2 - (√7)2}
⇒ 1/y = (√8 - √7)/(8 - 7)
∴ 1/y = √8 - √7
দেওয়া আছে,
y = √8 + √7
⇒ 1/y = 1/(√8 + √7)
⇒ 1/y = (√8 - √7)/(√8 + √7)(√8 - √7)
⇒ 1/y = (√8 - √7)/{(√8)2 - (√7)2}
⇒ 1/y = (√8 - √7)/(8 - 7)
∴ 1/y = √8 - √7
এখন, y + 1/y = (√8 + √7) + (√8 - √7)
= 2√8 = 2 × 2√2 = 4√2
এখন,
y3 + (1/y3)
= (y + 1/y)3 - 3(y)(1/y)(y + 1/y)
= (y + 1/y)3 - 3(y + 1/y)
= (4√2)3 - 3(4√2)
= (43)(√2)3 - 12√2
= 64(2√2) - 12√2
= 128√2 - 12√2
= 116√2
সুতরাং, নির্ণেয় মান হলো 116√2
0
Updated: 1 month ago
log3√254√2 + log2√264 = ?
Created: 1 month ago
A
12
B
10
C
7
D
9
প্রশ্ন: log3√254√2 + log2√264 = ?
সমাধান:
log3√254√2 + log2√264
= log3√2(3√2)3 + log2√2(2√2)4
= 3 + 4
= 7
এখানে
54√2 = 27 × 2√2
= 33 ×(√2)3
= (3√2)3
64 = 26
= 24 × {(√2)2}2
= 24 × (√2)4
= (2√2)4
0
Updated: 1 month ago
(3, 2) এবং (5, 4) বিন্দু দুইটির দুরত্ব কত?
Created: 1 month ago
A
4
B
3
C
3√2
D
2√2
প্রশ্ন: (3, 2) এবং (5, 4) বিন্দু দুইটির দুরত্ব কত?
সমাধান:
দেওয়া আছে,
(3, 2) এবং (5, 4)।
আমরা জানি,
দূরত্ব, d =√(x2 - x1)2 + (y2 - y1)2
এখানে,
x1 = 3, y1 = 2, x2 = 5, y2 = 4
∴ d =√{(5 - 3)2 + (4 - 2)2}
= √{(2)2 + (2)2}
= √(4 + 4)
= √8
= 2√2
0
Updated: 1 month ago
A solution contains 25% sugar by weight is made sweeter by doubling the amount of sugar. The percent of sugar, by weight, in the new solution is-
Created: 2 months ago
A
33.33%
B
32%
C
40%
D
23.27%
Question: A solution contains 25% sugar by weight is made sweeter by doubling the amount of sugar. The percent of sugar, by weight, in the new solution is-
Solution:
let, solution is 100 unit
amount of sugar = 100 × 25%
= 100 × (25/100)
= 25 unit
by doubling, amount of sweet = 50 unit
∴ solution now = 100 + 25 = 125 unit
∴ percent of sugar = {(50 × 100)/125}% = 40%
0
Updated: 2 months ago
