Question

a-b=4 and a+b=6;find ab

Answer 1

$\huge{\mathfrak{\underline{\underline{Answer:-}}}}$

$\large{\bf{a \:-\:b\: = \: 4...... <strong>[</strong><strong>1</strong><strong>]</strong>}}$

$\large{\bf{a \:+\:b\: = 6.......<strong>[</strong><strong>2</strong><strong>]</strong>}}$

$\huge{\mathfrak{\underline{\underline{Explanation:-}}}}$

$\large{\mathtt{ a \: = \: 4 \:+\:b \:\:[{From<strong> </strong>\: eq<strong> </strong>\:1]}}}$

$\large{\mathbf{\star{ Put \:value \: of \:a \:in \: eq \:2}}}$

$\LARGE{\mathtt{ 4 \:+\:b\:+\:b\:=\:6}}$

$\large{\mathtt{2b \:=\:2}}$

$\large{\rightarrow{\mathtt{ b \:=\:2/2}}}$

$\large{\rightarrow{\mathtt{ b \:=\:1}}}$

$\huge{\bigstar{\boxed{\red{b\: = \: 1 }}}}$

$\large{\bf{\star{Put \:value\:of \: b \: in \:eq \:1}}}$

$\large{\bf{ a \:-\:1 \:=\:4}}$

$\large{\bf{ a \:=\:4\:+\:1}}$

$\large{\bf{a= \: 5 }}$

$\huge{\bigstar{\boxed{\red{\: = \: 5 }}}}$

Answer 2

Answer :-

The value of ab is 5.

Solution :-

We know that

(a + b)² = (a - b)² + 4ab

Here

• a + b = 6

• a - b = 4

By substituting the values in the identity

⇒ (6)² = (4)² + 4ab

⇒ 36 = 16 + 4ab

⇒ 36 - 16 = 4ab

⇒ 20 = 4ab

⇒ 20/4 = ab

⇒ 5 = ab

⇒ ab = 5

Alternate

We know that

(a + b)² = a² + b² + 2ab

Here

• a + b = 6

By substituting the values in the identity

⇒ (6)² = a² + b² + 2ab

⇒ 36 = a² + b² + 2ab

⇒ 36 - 2ab = a² + b² ---(1)

We know that

(a - b)² = a² + b² - 2ab

Here

• a - b = 4

By substituting the values in the identity

⇒ (4)² = a² + b² - 2ab

⇒ 16 = a² + b² - 2ab

⇒ 16 + 2ab = a² + b² ---(1)

From (1) & (2)

⇒ 16 + 2ab = 36 - 2ab

⇒ 2ab + 2ab = 36 - 16

⇒ 4ab = 20

⇒ ab = 20/4

⇒ ab = 5

Therefore the value of ab is 5.