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What is the history of Vedic mathematics?

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Vedic Mathematics was rediscovered by Bharati Krishna Tirthaji in the early 20th century, based on ancient Indian texts called the Vedas.
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The Govt. is supposing to introduce Vedic Maths in school education (curriculum) - Is it right or wrong? -
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What is value of a & b.. in each case,

If a^b + b^a=45

If a^b X b^a=45

If a^b - b^a=45

1^44+44^1=45 So, a=1 & b=44 1^45*45^1=45 So, a=1 & b=45 46^1-1^46=45 So, a=46 & b=1
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