Question

Ax + By =5
Ax²+ By = 10
AX + By =50
AX + By = 130
13(x + y - xy) = 120(ATB)=?​

Answer 1

Required Answer:-

Given:

1. ax + by = 5
2. ax² + by = 19
3. ax³ + by³ = 50
4. ax⁴ + by⁴ = 130

To find:

• The value of 13(x + y - xy) - 120(a + b)

Solution:

We have,

➡ ax + by = 5 ......(i)

➡ ax² + by² = 10 ......(ii)

➡ ax³ + by³ = 50 .......(iii)

➡ ax⁴ + by⁴ = 130 ........(iv)

To solve this question, we have to find out the values of the following.

1. x + y = ?
2. xy = ?
3. a + b = ?

★ Let's start solving.

Multiplying both sides of equation (ii) by (x + y), we get,

➡ (ax² + by²)(x + y) = 10(x + y)

➡ ax³ + ax²y + bxy² + by³ = 10(x + y)

➡ ax³ + by³ + xy(ax + by) = 10(x + y)

Substituting the values of ax³ + by³ and ax + by, we get,

➡ 50 + 5xy = 10(x + y) .......(v)

Again,

Multiplying both sides of equation (iii) by (x + y), we get,

➡ (ax³ + by³)(x + y) = 50(x + y)

➡ ax⁴ + by⁴ + ax³y + bxy³ = 50(x + y)

➡ ax⁴ + by⁴ + xy(ax² + by²) = 50(x + y)

Again, substituting the values, we get,

➡ 130 + 100xy = 50(x + y) .......(vi)

Multiplying equation (v) by 2, we get,

➡ 100 + 100xy = 20(x + y) .......(vii)

Subtracting (vii) from (vi), we get,

➡ 30 = 30(x + y)

➡ x + y = 1 (★ Remember this)

Substituting the value of x + y in equation (v), we get,

➡ 50 + 5xy = 10

➡ 5xy = -40

➡ xy = -8 (★ Remember this)

Now, multiply both sides of equation (i) by (x + y). We get,

➡ (ax + by)(x + y) = 5(x + y)

➡ ax² + by² + axy + byx = 5(x + y)

Substitute all the values.

➡ 10 + xy(a + b) = 5

➡ -8(a + b) = -5

➡ (a + b) = -5/-8

➡ a + b = 5/8 (★ Remember this)

Thus,

13(x + y - xy) - 120(a + b)

= 13(1 - (-8)) - 120 × ⅝

= 13 × 9 - 75

= 117 - 75

= 42

Hence,

★ The value of 13(x + y - xy) - 120(a + b) is 42.

Answer:

• 13(x + y - xy) - 120(a + b) = 42.

Answer 2

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