Question

(4.23)²-(2.71)²/4.29-2.71

Answer 1

$\underline{\textbf{Given:}}$

$\mathsf{\dfrac{(4.23)^2-(2.71)^2}{4.23-2.71}}$

$\underline{\textbf{To find:}}$

$\textsf{The value of}$

$\mathsf{\dfrac{(4.23)^2-(2.71)^2}{4.23-2.71}}$

$\underline{\textbf{Solution:}}$

$\textsf{Consider,}$

$\mathsf{\dfrac{(4.23)^2-(2.71)^2}{4.23-2.71}}$

$\textsf{Using the algebraic identity,}$

$\boxed{\mathsf{a^2-b^2=(a-b)(a+b)}}$

$\mathsf{=\dfrac{(4.23-2.71)\,(4.23+2.71)}{4.23-2.71}}$

$\mathsf{=4.23+2.71}$

$\mathsf{=6.94}$

$\implies\boxed{\mathsf{\dfrac{(4.23)^2-(2.71)^2}{4.23-2.71}=6.94}}$

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Answer 2

SOLUTION

TO EVALUATE

$\displaystyle \sf{ \frac{ {(4.29)}^{2} - {(2.71)}^{2} }{4.29 - 2.71} }$

FORMULA TO BE IMPLEMENTED

We are aware of the formula that

$\sf{ {a}^{2} - {b}^{2} = (a + b)(a - b) }$

EVALUATION

$\displaystyle \sf{ \frac{ {(4.29)}^{2} - {(2.71)}^{2} }{4.29 - 2.71} }$

$\displaystyle \sf{ = \frac{ {(4.29 + 2.71)} {(4.29 - 2.71)} }{4.29 - 2.71} }$

$\displaystyle \sf{ = (4.29 + 2.71) }$

$\displaystyle \sf{ =7.00 }$

$\displaystyle \sf{ =7 }$

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