Question

Find the value of p if 51² - 49² =100p​

Answer 1

Step-by-step explanation:

51^2-49^2=(51+49)(51-49)=100x2=100p

p=2

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Answer 2

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EQUATION

$\boxed {51² - 49² = 100p}$

TO FIND ;

P value = ?¿

SOLUTION

$\boxed{ 51² - 49² = 100p}$

${: ⟹\sf{(50 + 1)^{2} - (50 - 1)^{2} = 100p}.............①}$

Need to solve step by step ;

$\sf{\:This \:is \:in \:the \:form \:of}$

${\bold{⇢(50 + 1)}^{2}}$

$\boxed{(a + b)² = a² + 2ab + b²}$

⇒a = 50

⇒b = 1

$\bold{⇢(50)² + 2(50)(1) + (1)²}$

$\sf{⇢2500 + 100 + 1}$.....................②

Now ;

${\bold{⇢(50 - 1)}^{2}}$

$\boxed{(a - b)² = a² - 2ab + b²}$

⇒a = 50

⇒b = 1

$\sf{⇢(50)² - 2(50)(1) + (1)²}$

$\sf{⇢2500 - 100 + 1}$.....................③

Now substitute eq② and eq③ in eq①

$\sf {➠~~(2500 + 100 + 1) - (2500 - 100 + 1) = 100p}$

$\sf {➠~~2500 + 100 + 1 - 2500 + 100 - 1 = 100p}$

$\sf {➠~~\cancel{2500} + 100 +~~ \cancel{1}~~ \cancel{- 2500} + 100~~ \cancel{- 1} = 100p}$

$\sf {➠~~200 = 100p}$

$\sf {➠~~\frac{200}{100} = p}$

$\sf {➠~~\frac{\cancel{200}^{2}}{\cancel{100}_{1}} = p}$

$\sf {➠~~2 = p}$

So the p value is $\boxed{p = 2}$