ਹੇਠ ਲਿਖਿਆਂ ਵਿੱਚੋਂ ਕਿਹੜਾ ਵਿਅੰਜਕ ਪ੍ਰਮੇਯ ਸੰਖਿਆਵਾਂ ਦੇ ਗੁਣਾ ਦੇ ਸਹਿਚਾਰਤਾ ਗੁਣ ਨੂੰ ਦਰਸਾਉਂਦਾ ਹੈ ?
Answers
Complete question :- ਹੇਠ ਲਿਖਿਆਂ ਵਿੱਚੋਂ ਕਿਹੜਾ ਵਿਅੰਜਕ ਪ੍ਰਮੇਯ
ਸੰਖਿਆਵਾਂ ਦੇ ਗੁਣਾ ਦੇ ਸਹਿਚਾਰਤਾ ਗੁਣ ਨੂੰ ਦਰਸਾਉਂਦਾ ? Which of the following expressions shows that rational numbers are associative under multiplication. निम्नलिखित में से ऐसे कौन
सा व्यंजक यह दर्शाता है कि परिमेय संख्याओं का गुणन सहचारी है ?
(Refer to image also for options.)
Solution :-
As we know that,
- Rational numbers follow the associative property for addition and multiplication.
Suppose x, y and z are rational numbers , then :
- for addition : x + (y + z)=(x + y) + z
- for multiplication : x(y * z) =(x *y)z.
checking Options one by one now, we get,
Option 1) :- (2/3)(-6/7 * 3/5) = (2/3 * -6/7) * 3/5
as we can see,
- » a(b * c) = (a * b) * c
Therefore, Option (1) shows associative property under multiplication.
Option 2) :- (2/3)(5/4 + 6/3) = (2/3 * 5/4) + (2/3 * 6/3)
as we can see,
- a*(b+c) = (a*b) + (a*c)
Therefore, Option (2) shows Distributive Property under multiplication.
Option 3) :- 4/5 * 5/7 = 5/7* 4/5
as we can see,
- a * b = b * a
Therefore, Option (3) shows Commutative Property under multiplication.
Option 4) :- 2/4 + (-2/4) = 0
as we can See,
- a * (-a) = 0
Therefore, Option (4) shows Inverse Property uinder addition .
Hence Option (1) shows associative Property under multiplication and is correct answer..
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if a^2+ab+b^2=25
b^2+bc+c^2=49
c^2+ca+a^2=64
Then, find the value of
(a+b+c)² - 100 = ...
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