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2 years ago

What is the expanded form of 43x65

Mathematics

1 answer:

bazaltina [42]2 years ago

8 0

43×65=2,795 expand form = 2,000+700+90+5=7,795

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3 years ago

If(√14/√7-2)-(√14/√7+2)=a√7+b√2 find the values of a and b where a and b are rational numbers

seraphim [82]

Answer:

a = 4/3 and b = 0

============================

<h2>Given expression:</h2>

$\dfrac{\sqrt{14} }{\sqrt{7}-2} -\dfrac{\sqrt{14} }{\sqrt{7}+2}$

<h2>Simplify it in steps:</h2>

Bring both fractions into common denominator:

$\dfrac{\sqrt{14} (\sqrt{7}+2)}{(\sqrt{7}-2)(\sqrt{7}+2)} - \dfrac{\sqrt{14} (\sqrt{7}-2)}{(\sqrt{7}-2)(\sqrt{7}+2)}$

Simplify:

$\dfrac{\sqrt{14} ((\sqrt{7}+2) - (\sqrt{7}-2))}{(\sqrt{7}-2)(\sqrt{7}+2)} =$

$\dfrac{\sqrt{14} (\sqrt{7}+2 - \sqrt{7}+2)}{(\sqrt{7}-2)(\sqrt{7}+2)} =$

$\dfrac{4\sqrt{14} }{(\sqrt{7}-2)(\sqrt{7}+2)} =$

$\dfrac{4\sqrt{14} }{(\sqrt{7})^2-2^2} =$

$\dfrac{4\sqrt{14} }{7-4} =$

$\dfrac{4}{3} \sqrt{14} }$

Compare the result with given expression to get:

a = 4/3 and b = 0

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