Solve the following sums: (a) Find the value of 34²-21². (b) If a=5-2√5, then find a².
Answers
Answer:
Answer:715
Answer:715Step-by-step explanation:
Answer:715Step-by-step explanation:34^2 - 21^2 = 1156-441= 715
Answer:715Step-by-step explanation:34^2 - 21^2 = 1156-441= 715a^2 = 0.527
The correct answers area)The value of 34²-21² is 715 and b) The value of a² is 45 - 20√5.
Given:
a) The expression 34²-21²
b) a = 5-2√5
To Find:
a) The value of 34²-21².
b) The value of a².
Solution:
a) We have been asked to find the value of 34²-21².
To solve this problem, we will use the concept
a² - b² = (a - b)(a + b)
By comparing with the given question:
a = 34 and b = 21
∴ 34²-21² = (34 - 21)(34 + 21) = 13 x 55 = 715
∴ The value of 34²-21² is 715.
b) We have been asked to find the value of a², if a = 5-2√5
⇒ a² = (5-2√5)² .....................(I)
To solve this problem, we will use the concept
(x - y)² = x² - 2xy + y²
By comparing (I) to the above equation, we have
x = 5 and y = 2√5
∴ a² = (5-2√5)² = 5² - 2(5)(2√5) + (2√5)² = 25 - 20√5 + 20
⇒ a² = 45 - 20√5.
∴ The value of a² is 45 - 20√5.
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