The (a + b + c)2 formula is used to find the sum of squares of three numbers without actually calculating the squares. a plus b plus c Whole Square Formula is one of the major algebraic identities. To derive the expansion of (a + b + c)^2 formula we just multiply (a + b + c) by itself to get A plus B plus C Whole Square. Let us learn more about the (a + b + c)2 formula along with solved examples.
- बंद नहीं हुए हैं 2000 रुपये के नोट, रिजर्व बैंक ने दी बड़ी जानकारी, आपके पास भी है तो अब क्या करें?
- Income Tax से आया 143 (1) नोटिस? घबराएं नहीं- समझिए क्या है मतलब और कैसे दें जवाब टैक्स एक्सपर्ट के मुताबिक, ऐसा नोटिस हर करदाता के पास आता है. अगर आपके पास ऐसा नोटिस नहीं आता है तो आप मान सकते हैं कि आपका रिटर्न प्रोसेस (IT Return processed) नहीं किया गया है. एप में देखें सबसे आम नोटिस इनकम टैक्स (Income tax notice) के सेक्शन 143(1) के तहत भेजा जाता है. (PTI)
- 50+ ज़िंदगी शायरी हिंदी में | Zindagi Shayari in Hindi, Urdu, Sad, & 2 Line Shayari
- भारत में सड़क सुरक्षा नियमों की सूची
- मीटर को फुट में बदलें
What Is (a + b + c)2 Formula?
We just read that by multiplying (a + b + c) by itself we can easily derive the (a + b + c)2 formula. Let us see the expansion of (a + b + c)2 formula. (a + b + c)2 = (a + b + c)(a + b + c) (a + b + c)2 = a2 + ab + ac + ab + b2 + bc + ca + bc + c2 (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca (a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)
Let us see how to use the (a + b + c)2 formula in the following section.
Examples on (a + b + c)2 Formula
Let us take a look at a few examples to better understand the A plus B plus C Whole Square Formula
Xem thêm : विलोम शब्द, Opposite words in Hindi 500 examples
Example 1: Find the value of a2 + b2 + c2 if a + b + c = 20 and ab + bc + ca = 20 using (a + b + c)2 formula.
Solution:
To find: a2 + b2 + c2 Given that: a + b + c = 20 ab + bc + ca = 2 Using the (a + b + c)2 formula, a2 + b2 + c2 = (a + b + c)2 – 2(ab + bc + ca) a2 + b2 + c2 = (20)2 – 2(20) = 400 – 40 = 360
Answer: a2 + b2 + c2 = 360.
Example 2: Find the value of a2 + b2 + c2 if a + b + c = 5, 1/a + 1/b + 1/c = 3 and abc = 4 using A plus B plus C Whole Square Formula.
Solution:
Xem thêm : Convert Bigha to Square Feet
To find: a2 + b2 + c2 Given that: a + b + c = 5 … (1) 1/a + 1/b + 1/c = 3 … (2) abc = 4 … (3) Multiplying equations (2) and (3), abc (1/a + 1/b + 1/c) = (4)(3) bc + ca + ab = 12 Using the (a + b + c)2 formula, a2 + b2 + c2 = (a + b + c)2 – 2(ab + bc + ca) a2 + b2 + c2 = (5)2 – 2(12) = 25 – 24 = 1
Answer: a2 + b2 + c2 = 1
Example 3: Find the value of a2 + b2 + c2 if a + b + c = 200 and ab + bc + ca = 10000 using (a + b + c)2 formula.
Solution:
To find: a2 + b2 + c2 Given that: a + b + c = 200 ab + bc + ca = 10000 Using the a2 + b2 + c2 formula, a2 + b2 + c2 = (a + b + c)2 – 2(ab + bc + ca) a2 + b2 + c2 = (200)2 – 2(10000) = 40000 – 20000 = 20000
Answer: a2 + b2 + c2 = 20000.
Nguồn: https://tromino.eu
Danh mục: शिक्षा
