Question

3x +4y= 25 and xy=10. find 9x² +16y²​

Answer 1

Step-by-step explanation:

Given :-

3x+4y = 25

xy = 10

To find :-

The value of 9x²+16y².

Solution :-

Given that

3x+4y = 25 --------(1)

xy = 10 -------------(2)

On squaring (1) both sides then

(3x+4y)² = 25²

LHS is in the form of (a+b)²

Where, a = 3x and b = 4y

We know that

(a+b)² = a²+2ab+b²

Therefore,

(3x)²+2(3x)(4y)+(4y)² = 25×25

=> 9x²+24xy+16y² = 625

=> 9x²+16y²+24xy = 625

=> 9x²+16y²+24(10) = 625 (From (1))

=> 9x²+16y² +240 = 625

=> 9x²+16y² = 625-240

=> 9x²+16y² = 385

Answer :-

The value of 9x²+16y² is 385

Used Identity :-

→ (a+b)² = a²+2ab+b²

Answer 2

★ Given :-

⠀

• 3x + 4y = 25.. (eq. 1)
• xy = 10...(eq. 2)

⠀

★ To Find :-

⠀

• The value of 9x² + 16y²

⠀

★ Formula Used :-

⠀

$\quad \bigstar \: \underline{ \boxed{ \sf (a + b) {}^{2} = {a}^{2} + 2ab + {b}^{2} }}$

⠀

★ Solution :-

⠀

Squaring on both sides we get :-

⠀

$\sf \longrightarrow \: (3x + 4y) {}^{2} = {25}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf \longrightarrow \:9 {x}^{2} + 2(3x \times 4y) + {16y}^{2} = 625 \\ \\ \sf \longrightarrow \: {9x}^{2} + 24xy + {16y}^{2} = 625 \: \: \: \: \: \: \: \: \: \: \:$

⠀

Now, we will put the value of xy i.e. 10, we get :-

⠀

$\sf \longrightarrow \: {9x}^{2} + 24 \times 10 + {16y}^{2} = 625 \\ \\\sf \longrightarrow \: {9x}^{2} + {16y}^{2} = 625 - 240 \: \: \: \: \: \: \: \: \\ \\ \sf \longrightarrow \: {9x}^{2} + {16y}^{2} = 385 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\rule{200pt}{}$