Question

pls solve this question

Answer 1

Given: (1/2 + √7) + (1/√7 + √10) + ... + (1/√28 + √31)

= (1/√4 + √7) + (1/√7 + √10) + ... + (1/√28 + √31)

On rationalizing, we get

= (1/√4+√7)*(√4-√7/√4-√7) + (1/√7+√10)*(√7-√10)/(√7-√10) + ... + (1/√28+√31)*(√28-√31/√28-√31)

= [(√4-√7/(√4)² - (√7)²] + [(√7-√10)/(√7)²-(√10)^2] + .. [(√28-√31)/(√28)²-(√31)²]

= [(√4 - √7)/4-7] + [(√7-√10)/7-10)] +...+ [(√28-√31/28-31)]

= (√4 - √7)/-3] + [(√7 - √10)/-3)] +... + [(√28 - √31)/-3]

= [(√7 - √4)/3] + [(√10 - √7)/3] + .... +[(√31-√28)]/3]

= 1/3[√7 - √4 + √10 - √7 + √31 - √28]

= 1/3[√31 - √4]

= √31 - √4/3

= (√31 - 2)/3.

Hope it helps!

Answer 2

Answer:

4

Step-by-step explanation:

Answer is explained below.